19. Q19
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Similar Question 1
<p>Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.</p><p><code class='latex inline'>\displaystyle x+4 y=8\\y+2 x=0 </code></p>
Similar Question 2
<p>Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.</p><p><code class='latex inline'>\displaystyle 2 y=3 x-1\\8 y-4=12 x </code></p>
Similar Question 3
<p> Write an equation that forms a system of equations with <code class='latex inline'> x+y=4 </code> , so that the system has</p><p>a) no solution</p><p>b) infinitely many solutions</p><p>c) one solution</p>
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>Solve the following systems of equations, and explain the nature of each intersection:</p><p><code class='latex inline'>\displaystyle \begin{array}{lllll} &2x + y &= 3 \\ &2x + y &= 4 \\ \end{array} </code></p>
<p> Consider this system of linear equations:<br> <code class='latex inline'>\displaystyle \begin{array}{cccc} & 2x + y = 7\\ &8x + 4y = 10\\ \end{array} </code> </p><p><strong>a)</strong> Can you create an equivalent system that contains only one variable? </p><p><strong>b)</strong> What does your result for part a) suggest about the solution to the original system? </p><p><strong>c)</strong> What does your result for part a) suggest about the graphs of both lines? </p>
<p>Explain how you know that this system of equations has no solution.</p><p><code class='latex inline'>\displaystyle \begin{array}{lllll} &15 -6y = 9x\\ &3x + 2y = 8 \end{array} </code></p>
<p>For the first equation in the system of linear equations below, write an equivalent equation without denominators. Then solve the system.</p><p><code class='latex inline'>\displaystyle \left\{\begin{array}{l}\frac{x}{5}+\frac{y}{3}=6 \\ x-2 y=8\end{array}\right. </code></p>
<p>Use the equation <code class='latex inline'>3x + 4y= 2</code></p><p>Write another equation that will create a linear system with each number of solutions.</p><p>i) none</p><p>ii) one</p><p>iii) infinitely many</p>
<p>Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.</p><p><code class='latex inline'>\displaystyle x+4 y=8\\y+2 x=0 </code></p>
<p>Solve the following systems of equations, and explain the nature of each intersection:</p><p><code class='latex inline'>\displaystyle \begin{array}{lllll} &7x -3y &= 9 \\ &35x - 15y &= 45 \end{array} </code></p>
<p>a) Can you solve the linear system <code class='latex inline'>y=3x-2</code> and <code class='latex inline'>6x-2y-4=0</code>? Explain your reasoning.</p><p>b) Can you solve the linear system <code class='latex inline'>y=4x-3</code> and <code class='latex inline'>8x-2y+ 5 =0</code>?</p><p>Explain your reasoning.</p><p>c) Explain how you can tell, without solving, how many solutions a linear system has.</p>
<p>Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.</p><p><code class='latex inline'>\displaystyle 2 y-x-4=0\\3 x-6 y-12=0 </code></p>
<p>Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.</p><p><code class='latex inline'>\displaystyle \begin{aligned} & 3 c+d=4 \\ & 6 c+2 d=8 \end{aligned} </code></p>
<p>Solve each system of equations by elimination. Check each solution.</p><p><code class='latex inline'>\displaystyle 2 x+5 y=3 </code></p><p><code class='latex inline'>\displaystyle 4 x+10 y-6=0 </code></p>
<p>Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.</p><p><code class='latex inline'>\displaystyle x+y=2\\3 x=6-3 y </code></p>
<p> Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.</p><p><code class='latex inline'>\displaystyle 3 x-y=0\\6 x-2 y=3 </code></p>
<p> Write an equation that forms a system of equations with <code class='latex inline'> x+y=4 </code> , so that the system has</p><p>a) no solution</p><p>b) infinitely many solutions</p><p>c) one solution</p>
<p>Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.</p><p><code class='latex inline'>\displaystyle x+2 y-7=0\\3 x+6 y-14=0 </code></p>
<p> Write a system of equations that has the point <code class='latex inline'> (3,2) </code> as</p><p>a) the only solution</p><p>b) one of infinitely many solutions</p>
<p>Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.</p><p><code class='latex inline'>\displaystyle 2 y=3 x-1\\8 y-4=12 x </code></p>
<p>Solve each system of equations by elimination. Check each solution.</p><p><code class='latex inline'>\displaystyle 2 x-3 y=8 </code></p><p><code class='latex inline'>\displaystyle 4 x-6 y=10 </code></p>
<p>Without graphing, determine whether each system has one solution no solution, or infinitely many solutions.</p><p><code class='latex inline'>\displaystyle 4 x-2 y=0\\2 x-y=3 </code></p>
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