Algebra 1-1 DA
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5.2 Solving Systems of Equations by Substitution Homework
Solving a linear system by SUBSTITUTION
1.
2.
3.
4.
Solve one of the equations for one of its variables. (Usually x or y)
Substitute the expression from step 1 into the other equation and solve for the other variable.
Substitute the value from step 2 into the revised equation from step 1 and solve.
Check your solution into each original equation.
Solve using substitution.
1. 5x – 3y = -24
x = 3y
2. 6x + 2y = -18
y = -4x
3. y = -2x
3x – 4y = 11
4. x = y
-4x + 7y = 9
5. x + 2y = -5
x = 2y – 1
6. y = -4x + 7
3x – 2y = 8
7. 9x – y = 23
y = 3x + 7
8. -x + 8y = 20
x = 4 + 5y
9. y = x – 14
y = 2x – 10
10. y = 4x + 12
y = 2x – 8
11. y = -x + 5
2x + 2y = -4
12. 5x – y = 7
y = 5x – 7
13. x + 3y = 13
4x – y = 13
14. 3x – 5y = -16
x + 7y = -14
Determine if the ordered pair is a solution to the system of equations. Show work
15. 2x + 3y = -15
16. 3x – y = 4
x = -4y
y=x
(0, -5)
(1, -1)
17. x + 4y = -9
y = -2x + 3
(3, -3)
18. y = -x + 4
y = 2x - 5
(1, 3)
19. On a rural highway, a police officer sees a motorist run a red light at 40 mi/h and begins pursuit. At the
instant the police officer passes through the intersection at 60 mi/h, the motorist is 2 mi down the road. When
and where will the officer catch up to the motorist? Let x represent the number of hours and y represent the
number of miles.
a. Write a system of equations in two variables to model this situation.
b. Solve this system by the substitution method, and check the solution.
c. Explain the real-world meaning of the solution.
20. Last year you mowed grass and shoveled snow for 20 households. You earned $150 per household mowing
for the entire season and $200 per household shoveling for the entire season. If you earned a total of $3650 last
year, how many households did you mow and shovel for? Let x represent the number of households mowed and
y represent the number of households shoveled.
a. Write a system of equations in two variables to model this situation.
b. Solve this system by the substitution method, and check the solution.
c. Explain the real-world meaning of the solution.