1. Graphing and Elimination
Review for Quiz:
Sections 5.1 and 5.3
Solving Systems by
Graphing and Elimination

2. { Solve the system of equations by graphing: y = 2x – 8 y = x3
+ 0
Graph the first line:
 y-intercept: 8 on y-axis
 use slope = 2 =
2 up
1 right
Graph the second line:
 y-intercept: 0 on y-axis
 use slope =
2 up
3 right
Solution:
(6, 4)

3. { 2. Solve the system of equations by graphing: y = – x + 64 5
Graph the first line:
 y-intercept: 6 on y-axis
 use slope =
4 down
5 right
Graph the second line:
 Solve the equation for y.
y = – x – 4 4 5
 y-intercept:  4 on y-axis
Solution:
no solution
 use slope =
4 down
5 right

4. { 3. Solve the system of equations by graphing: y = x – 2 x – 3y = 61 3
Graph the first line:
 y-intercept: 2 on y-axis.
 slope =
1 up
3 right
Graph the second line:
 Solve the equation for y. 1
x  3y = 6
Give y a positive coefficient.
1x + 3y = 6
+1x x
3y = 1x  6
Solution:
infinite solutions
y = x  2 1 3
Same as first equation.

5. { 4. Solve the system of equations by graphing: x = –3 2x + 3y = 12
Graph the first line:
 x is always 3.
x y   
Graph the second line:
 Solve the equation for y.
2x + 3y = 12
y has a positive coefficient.
2x 2x
3y = 2x + 12
y-intercept:
4 on y-axis
Solution:
(3, 6)
y = x + 4 2 3
2 down
3 right
slope =

6. { 5. Solve the system of equations by elimination: 3x – 4y = 38
Add the equations:
8x = 16
 The variable y cancels out.
 Solve for x.
x = 2
Solve for the 2nd variable:
5x + 4y = 22
5(2) + 4y = 22
 Substitute x into either equation.
10 + 4y = 22
 Solve for y.
– –10
4y = 32
Solution: in alphabetical order.
Solution: (2, –8)
y = 8

7. { 6. Solve the system of equations by elimination: 6x + 5y = 39
Add the equations:
4y = 12
 The variable x cancels out.
 Solve for y.
y = 3
Solve for the 2nd variable:
6x + 5y = 39
6x + 5(3) = 39
 Substitute y into either equation.
6x + 15 = 39
 Solve for x.
–15 –15
6x = 24
Solution: in alphabetical order.
 6
Solution: (–4, 3)
x = 4

8. { 7. Find two numbers whose sum is 26 and whose difference is 14.
x + y = 26
x – y = 14
1x + y = 26
1x – y = 14
Write a system of equations:
Add the equations:
2x = 40
 The variable y cancels out.
 Solve for x.
x = 20
Solve for the 2nd variable:
x + y = 26
 Substitute x into either equation.
20 + y = 26
 Solve for y.
– –20
Solution:
y = 6
The numbers are 20 and 6.

9. { 8. Solve the system of equations by elimination: 2x + 7y = 53 - - +
Nothing cancels out yet :
4x = 36
 Take the opposite of either row.
 4
Add the equations:
x = 9
 The variable y cancels out.
 Solve for x.
2x + 7y = 53
Solve for the 2nd variable:
2(9) + 7y = 53
18 + 7y = 53
 Substitute x into either equation.
 Solve for y.
7y = 35
Solution: in alphabetical order.
Solution: (–9, –5)
y = 5

10. { 9. Solve the system of equations by elimination: 6x + 7y = 28
Nothing cancels out yet :
5y = 10
 Take the opposite of either row.
Add the equations:
y = 2
 The variable x cancels out.
 Solve for y.
6x + 7y = 28
Solve for the 2nd variable:
6x + 7(2) = 28
6x + 14 = 28
 Substitute y into either equation.
14 14
 Solve for x.
6x = 42
Solution: in alphabetical order.
 6
Solution: (7, 2)
x = 7

11. { 10. Solve the system of equations by elimination: 11x – 12y = 13
Nothing cancels out yet :
0 = 26
 Take the opposite of either row.
False
Add the equations:
 The variables x and y both cancel out.
Find the solution.
 False Statement: No Solution
Solution: No Solution