18. Q18
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Similar Question 1
<p>Solve the linear system graphically.</p><p> <code class='latex inline'> \displaystyle \begin{array}{lllll} & x + y = 2 \\ & x = 2y + 2 \\ \end{array} </code></p>
Similar Question 2
<p>The equations <code class='latex inline'>y = 2, y = 4x - 2</code>, and <code class='latex inline'>y = - 2x + 10</code> form the sides of a triangle.</p> <ul> <li>Graph the triangle, and determine the area of the triangle.</li> </ul>
Similar Question 3
<p>The equations <code class='latex inline'>y = 2, y = 4x - 2</code>, and <code class='latex inline'>y = - 2x + 10</code> form the sides of a triangle.</p> <ul> <li>Graph the triangle, and determine the area of the triangle.</li> </ul>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Decide whether the ordered pair is a solution to the given system of equations.</p><p><code class='latex inline'>(1, -2); y = 3x -5</code> and <code class='latex inline'>y = 2x - 4</code></p>
<p> Six cups of coffee and a dozen muffins originally cost <code class='latex inline'>\$15.35</code>. The price of a cup of coffee increases by <code class='latex inline'>10\%</code>. The price of a dozen muffins increases by <code class='latex inline'>12\%</code>. The new cost of six cups of coffee and a dozen muffins is <code class='latex inline'>\$17.06</code>. Determine the new price of one cup of coffee and a dozen muffins.</p>
<p>Willow bought <code class='latex inline'>3m</code> of denim fabric and 5m of cotton fabric.The total bill, excluding tax, was <code class='latex inline'>\$22</code>. Jared bought <code class='latex inline'>6 m</code> of denim fabric and <code class='latex inline'>2 m</code> of cotton fabric at the same store for <code class='latex inline'>\$28</code>.</p><p><strong>a)</strong> Write a linear system you can solve to determine the price of denim fabric and the price of cotton fabric.</p><p><strong>b)</strong> Solve your system using a graph.</p><p><strong>c)</strong> How much will <code class='latex inline'>8 m</code> of denim fabric and <code class='latex inline'>5 m</code> of cotton fabric cost?</p>
<p>Determine the point of intersection of <code class='latex inline'>9x+4y-19=0</code> with the pair <code class='latex inline'>3x - y - 11 = 0</code> and <code class='latex inline'>x + 2y + 1 = 0</code>. You can use a graphing device.</p>
<p>Solve each of the following systems of equations using a graph. </p> <ul> <li><code class='latex inline'>3x - 4y = -12</code> and <code class='latex inline'>2x - 3y = 64</code></li> </ul>
<p>The equations <code class='latex inline'>y = 2, y = 4x - 2</code>, and <code class='latex inline'>y = - 2x + 10</code> form the sides of a triangle.</p> <ul> <li>Graph the triangle, and determine the area of the triangle.</li> </ul>
<p>Decide whether the ordered pair is a solution to the given system of equations.</p><p><code class='latex inline'>(2, -1); 3x + 2y =4</code> and <code class='latex inline'>-x + 3y = -5</code></p>
<p>Solve the system of equations.</p><p><code class='latex inline'>y = 2x^2</code></p><p><code class='latex inline'>y = -3x + 5</code></p>
<p>Solve each linear system by graphing.</p><p><code class='latex inline'>y = 3x - 5</code></p><p><code class='latex inline'>y = -2x + 5</code></p>
<p>Solve each linear system by graphing.</p><p><code class='latex inline'>6x - 5y - 12 = 0</code></p><p><code class='latex inline'>-2x + 5y + 2 = 0</code></p>
<p>Solve each linear system by graphing.</p><p><code class='latex inline'>2x + y = 10</code></p><p><code class='latex inline'>y = x -2</code></p>
<p>Solve the linear system graphically.</p><p> <code class='latex inline'> \displaystyle \begin{array}{lllll} & y -x = 1 \\ & 2x - y = 1 \\ \end{array} </code></p>
<p>Solve each linear system by graphing.</p><p><code class='latex inline'>x + y = 3</code></p><p><code class='latex inline'>x - y = 7</code></p>
<p>Solve each linear system by graphing.</p><p><code class='latex inline'>y = 2x - 4</code></p><p><code class='latex inline'>3x + y = 6</code></p>
<p>Solve the system: <code class='latex inline'>x + y = 5</code> and <code class='latex inline'>3x + 4y = 12</code></p>
<p>Solve each linear system by graphing.</p><p><code class='latex inline'>x + y = 8</code></p><p><code class='latex inline'>4x - 2y = 8</code></p>
<p>The drama department of a school sold 679 tickets to the school play, for a total of <code class='latex inline'>\$3370</code>. Students paid <code class='latex inline'>\$4</code> for a ticket, and non-students paid <code class='latex inline'>\$7</code>. </p><p><strong>a)</strong> Write a linear system for this situation.</p><p><strong>b)</strong> How many non-students attended the play?</p><p>Solve the problem by graphing your system.</p> <p>For each graph:</p><p> Identify the point of intersection.</p><img src="/qimages/1474" /> <p>Decide whether the ordered pair is a solution to the given system of equations.</p><p><code class='latex inline'>(10, 5); x - y = 5</code> and <code class='latex inline'>y = 5x - 40</code></p> <p>Alex needs to rent a minivan for a week to take his band on tour. Easyvans charges <code class='latex inline'>\$230</code> plus <code class='latex inline'>\$0.10/km</code>. Cars for All Seasons charges <code class='latex inline'>\$150</code> plus <code class='latex inline'>\$0.22/km</code>.</p><p><strong>a)</strong> Write an equation for each rental company.</p><p><strong>b)</strong> Which rental company would you recommend to Alex if he was planning on driving <code class='latex inline'>700 km</code>.</p> <p>Joanna is considering two job offers. Phoenix Fashions offers$1500/month plus <code class='latex inline'>2.5\%</code> commission. Styles by Rebecca offers <code class='latex inline'>\$1250/month</code> plus <code class='latex inline'>5.5\%</code> commission.</p> <ul> <li>Which job should Joanna take if she is confident that she can sell more than <code class='latex inline'>\$9000</code></li> </ul>
<p>Use graphing to find the point of intersection of the lines <code class='latex inline'>y = 3x - 22</code> and <code class='latex inline'>y = 4x - 29</code>.</p>
<p>Joanna is considering two job offers. Phoenix Fashions offers <code class='latex inline'>\$1500</code>/month plus <code class='latex inline'>2.5\%</code> commission. Styles by Rebecca offers <code class='latex inline'>\$1250/month</code> plus <code class='latex inline'>5.5\%</code> commission.</p> <ul> <li>Create a linear system by writing an equation for each salary.</li> </ul>
<p>Decide whether the ordered pair is a solution to the given system of equations.</p><p><code class='latex inline'>(4, 4); x + y =5</code> and <code class='latex inline'>2x + 2y = 8</code></p>
<p>For the graph:</p><p>Identify the point of intersection.</p><img src="/qimages/1475" />
<p>Joanna is considering two job offers. Phoenix Fashions offers <code class='latex inline'>\$1500/month</code> plus <code class='latex inline'>2.5\%</code> commission. Styles by Rebecca offers <code class='latex inline'>\$1250/month</code> plus <code class='latex inline'>5.5\%</code> commission.</p> <ul> <li>What value of sales would result in the same total salary for both jobs?</li> </ul>
<p>At Jess’s Java, a new blend of coffee is featured each week. This week, Jess is creating a low-caffeine espresso blend from Brazilian and Ethiopian beans. She wants to make 200 kg of this blend and sell it for <code class='latex inline'>\$15/kg</code>. The Brazilian beans sell for <code class='latex inline'>\$12/kg</code>, and the Ethiopian beans sell for <code class='latex inline'>\$17/kg</code>. How many kilograms of each kind of bean must Jess use to make <code class='latex inline'>200 kg</code> of her new blend of the week?</p> <p>For the graph:</p> <ul> <li> Identify the point of intersection.</li> </ul> <img src="/qimages/1473" /> <p>When Arthur goes fishing, he drives 393 km from his home in Ottawa to a lodge near Temagami. He travels at an average speed of 70 km/h along the highway to North Bay and then at 50 km/h on the narrow road from North Bay to Temagami. The journey takes him 6 h.</p><p><strong>a)</strong> Write two equations to describe this situation.</p><p><strong>b)</strong> Graph your equations to determine the distance from North Bay to Temagami.</p> <p>Solve each system by graphing. Check your solution.</p><p><code class='latex inline'>\displaystyle y=2 x </code></p><p><code class='latex inline'>\displaystyle y=-2 x+8 </code></p> <p>Austin is creating a new “trailmix” by combining two of his best-selling blends-a pineapple–coconut–macadamia mix that sells for <code class='latex inline'>\$18/kg</code> and a banana–papaya–peanut mix that sells for <code class='latex inline'>\$10/kg</code>. He is making <code class='latex inline'>80 kg</code> of the new mix and will sell it for <code class='latex inline'>\$12.50/kg</code>. Austin uses the graph shown at the right to determine how much of each blend he needs to use.</p><p><strong>a)</strong> Write the equations of the linear relations in the graph.</p><p><strong>b)</strong> From the graph, how much of each blend will Austin use?</p><img src="/qimages/1476" />
<p>Solve the linear system <code class='latex inline'>y= 2x- 1, 4x- 3y= 7</code>,and <code class='latex inline'>6x+ y+ 17= 0</code>.</p>
<p>Solve the linear system graphically.</p><p> <code class='latex inline'> \displaystyle \begin{array}{lllll} & x + y = 2 \\ & x = 2y + 2 \\ \end{array} </code></p>
<p>Determine the values of <code class='latex inline'>c</code> and <code class='latex inline'>d</code> if <code class='latex inline'>9x + 4y - 19 = 0</code> is written in the form <code class='latex inline'>c(3x - y - 11) + d(x + 2y + 1) = 0</code>. Is there only one possible answer for <code class='latex inline'>(c, d)</code>? Explain.</p>
<p>Solve the system of equations.</p><p><code class='latex inline'>y = \sqrt{x}</code></p><p><code class='latex inline'>y = x - 1</code></p>
<p>Solve the linear system <code class='latex inline'>3x - y - 11 = 0</code> and <code class='latex inline'>x + 2y + 1 = 0</code>.</p>
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