Systems Of Linear Equations Worksheets With Answer Key Page 36
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405.4
5.4
Solving Special Systems of Linear Equations
(pp. 224–231)
y = −5x − 8
a. Solve the system.
Equation 1
y = −5x + 4
Equation 2
Solve by substitution. Substitute − 5x + 4 for y in Equation 1.
y = − 5x − 8
Equation 1
− 5x + 4
= − 5x − 8
Substitute − 5x + 4 for y.
✗
4 = − 8
Add 5x to each side.
The equation 4 = − 8 is never true. So, the system of linear equations
has no solution.
1
b. Solve x + 1 =
x + 3 using a graph. Check your solution.
—
3
Step 1: Write a system of linear equations using each side of the equation.
1
x + 1 =
x + 3
—
3
1
y = x + 1
y =
x + 3
—
3
Step 2: Graph the system.
y = x + 1
1
y =
x + 3
—
3
y
Check
1
1
y
x
3
x + 1 =
x + 3
—
3
(3, 4)
3
2
?
1
+ 1 =
(3) + 3
3
—
y
x
1
3
4
3
2
1
2
3
4
x
✓
1
4 = 4
2
The graphs intersect at (3, 4).
So, the solution is x = 3.
Solve the system of linear equations. Check your solution.
8. x + 2y = − 5
9. 3x − 2y = 1
10. 8x − 2y = 16
x − 2y = − 5
9x − 6y = 3
− 4x + y = 8
11. Use a graph to solve 2x − 9 = 7x + 11. Check your solution.
Chapter Review
235
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