1. Solving for x and y when you have two equations
Systems of equations
Solving for x and y when you
have two equations

2. Solve the system of equations
There is only one number for x, and one number for y, that can be plugged into BOTH equations and make the equation true.
2x + y = 9
x = 3y + 8
(5, -1)
(-9, -8)
(4, 1)
(10, 3)
Let’s try the x and y values for the first answer:
2(5) + (-1) = and (5) = 3(-1) + 8
5 =
10 + (-1) = 9
5 = 5
= 9
9 = 9

3. Solve for x and y: y = 2x 4x + 2y = 8 4x + 2y = 8 y = 2x x y 4 1 2 x y4 1 2 x y 1 2
When x =1, y = 2 for both equations. Therefore the solution for the system of equations is (1, 2). Notice that the graphs of the lines cross at (1, 2).

4. Solve for x and y: y = x + 3 y = -x - 2
It looks like they cross at the point (-2.5, .5 )
y = x + 3
Where they cross is the solution for x and y.
Plug in -2.5 for x
and .5 for y
to see if they work in BOTH equations
y = -x -2

5. Solve for x and y: y = x + 3 y = -x - 2
It looks like they cross at the point (-2.5, 0.5)
Plug in -2.5 for x
and 0.5 for y
y = x + 3
0.5 =
.5 =
0.5 = 0.5
YES
y = -x - 2
0.5 = -(-2.5) - 2
.5 =
0.5 = 0.5
YES
y = x + 3
y = -x -2
Solution:
x = y = 0.5

6. Find the solutions for x and y
The lines do not have any (x, y) points in common.
Parallel lines do not cross.
NO SOLUTION FOR X AND Y
y = x + 3
y = x - 2

7. Find the solutions for x and y
x = y = 1 1
(1, 1)