Solve each system by graphing. Check your solutions.
\displaystyle
y=x-5\\y=3-x
Solve each system by graphing. Check your solutions.
\displaystyle
m+2 n=2\\3 m+2 n=-6
Solve each system by graphing. Check your solutions.
\displaystyle
p-q=1\\p+2 q=7
Solve each system by graphing. Check your solutions.
\displaystyle
2 x+y=2\\2 x+y+4=0
Solve each system by graphing. Check your solutions.
\displaystyle
x-y-4=0\\5 x-y-8=0
Solve each system by graphing. Check your solutions.
\displaystyle
a+b=4\\3 a=12-3 b
Solve each system by graphing. Check your solutions.
\displaystyle
3 x-2 y=-8\\x-2 y=-4
Solve each system by graphing. Check your solutions.
\displaystyle
2 x-y=-4\\2 x+y=6
Solve each system graphically.
\displaystyle
4 x+3 y=1\\4 x-3 y=14
Solve each system graphically.
\displaystyle
3 x+y=1\\x+4 y=3
Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.
\displaystyle
\begin{aligned} & 3 c+d=4 \\ & 6 c+2 d=8 \end{aligned}
Without graphing, determine whether each system has one solution no solution, or infinitely many solutions.
\displaystyle
4 x-2 y=0\\2 x-y=3
Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.
\displaystyle
x+5 y=9\\x-y=3
Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions.
\displaystyle
x+2 y-7=0\\3 x+6 y-14=0
The two largest deserts in the world are the Sahara Desert and the Australian Desert. The sum of their areas is 13 million square kilometres. The area of the Sahara Desert is 5 million square kilometres more than the area of the Australian Desert. Solve the following system graphically to find the area of each desert, in millions of square kilometres.
\displaystyle
s+a=13\\s=a+5
Profit A company manufactures and sells paddles. Its manufacturing
costs are \$ 500 , plus \$ 10 per paddle. The company sells the paddles for \$ 18 .
The cost and revenue can be represented by the following system of equations.
Dollar Cost: \quad d=500+10 p
Dollar Revenue: \displaystyle
d=18 p
a) What does each variable represent?
b) Solve the system graphically.
c) How many paddles must be sold for the company to make a profit?
Solve each system by substitution. Check each solution.
\displaystyle
y=6-2 x\\3 x+2 y=10
Solve each system by substitution. Check each solution.
\displaystyle
3 x+y-2=0\\5 x+2 y-3=0
Solve each system by substitution. Check each solution.
\displaystyle
3 s+5 t=2\\s+4 t=-4
Solve each system by substitution. Check each solution.
\displaystyle
x+4 y=-3\\2 x+8 y=-6
Solve each system by substitution. Check each solution.
\displaystyle
3 x+2 y=9\\-x+3 y=8
Solve each system by substitution. Check each solution.
Solve each system by substitution. Check each solution.
Solve each system by substitution. Check each solution.
Simplify each system, and then solve it by substitution. Check each solution.
\displaystyle
2(x-1)+y=2\\3 x-4(y+3)=5
Simplify each system, and then solve it by substitution. Check each solution.
Which method would you use to solve each system of equations? Explain. Then, solve and check each system.
Which method would you use to solve each system of equations? Explain. Then, solve and check each system.
Which method would you use to solve each system of equations? Explain. Then, solve and check each system.
Which method would you use to solve each system of equations? Explain. Then, solve and check each system.