Answer
1. Three graphs were created and the solution is identified on the graphs.
Solutions are
System A is upper right (1, 2)
System B is lower left ( 5, -6)
System C is lower right ( 1/2, 3)
2. Find the sum or difference. When you solve this way, you want either the x or the y values to cancel out so you can solve for one variable.
System A is already set up this way. See how the 4x and -4x cancel out?
4x + 3y = 10
-4x +5y = 6
__________
8y = 16
Divide both sides by 8 to solve
8/8 y = 16/8
y = 2
Sub y = 2 into either equation to solve x
4x + 3y = 10
4x + (3)(2) = 10
4x + 6 = 10
Subtract 6 from both sides to isolate variable
4x + 6 -6 = 10 - 6
Simplify
4x = 4
Divide both sides by 4 to solve
4/4 x = 4/4
x = 1
Solution pair is (1, 2)
System B has the y values ready to cancel out
2x + y = 4
x - y = 11
__________
3x .= 15
Divide both sides by 3 to solve for x
3/3 x = 15/3
x = 5
Sub x = 5 into either equation to solve for y
5 - y = 11
Subtract 5 from both sides
5-5 -y = 11 - 5
-y = 6
y = -6
Solution pair is ( 5, -6 )
System C - we need to multiply the second equation by -1 to create the cancel of x
8x + 11y = 37
8x + y = 7
-1. -1. -1
___________
-8x -y = -7
Now we can cancel the x’s and solve
8x + 11y = 37
-8x -y = -7
___________
10y = 30
Divide both sides by 10
10/10 y = 30/10
Simplify
y = 3
Now sub y = 3 into either equation to solve x
8x + (11)(3)= 37
8x + 33 = 37
Subtract 33 from both sides
8x + 33 - 33 = 37 - 33
8x = 4
Divide both sides by 8 to solve for x
8/8 x = 4/8
x = 4/8
Simplify
x = 1/2
Solution pair is ( 1/2, 3)
3. The graphs show the x horizontal line and y vertical line from the coordinate solution intersect with the lines of the two equations.
This was a lot of work. I hope it made sense.