Algebra 1-1 DA
5.2 Notes – Solving Systems of Equations by Substitution
Review Solving by graphing and the next step.
Solve the system by graphing.
4x – 3y = 9
x + 2y = -4
Describe how to find the solution to a system of
equations when graphing?
What are the drawbacks to solving a system of equations by graphing?
Determine if the ordered pair is a solution to the system of equations. Show work.
1. y = 2x – 7
2. 2x + 3y = -10
y = -x + 8
x = -4y
(4, 1)
(1, -4)
3. 2x – 3y = 13
y = 2x – 3
(-1, -5)
4. y = x + 8
y = -x – 4
(1, 9)
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. 3x – 2y = -8
x = 2y
2. 2x – 5y = 21
x = -y
3. 2x + 7y = -4
x = 1 – 4y
4. y = 3x – 13
4x + 5y = 11
5. y = 4 + x
x – y = -4
6. 3x – y = -2
y = 3x + 2
7. 2x + 3y = 1
-3x + y = 15
8. 4x – 5y = -6
x + 2y = 5
9. x + y = 3
2y + 2x = 4
10. 8x + 2y = 13
4x + y = 4
11. x + 2y = -7
5x – y = -2
12. -2x + y = 6
x – 3y = 7
13. 4x – y = -20
3x + 2y = 7
14. 5x – 2y = -1
-x + 4y = -7
15. y = 3x – 5
y = -2x + 5
16. y = -x + 3
y = 2x – 12
17. y = 2x + 3
y = 2x + 3
18. y = -3x + 4
y = -3x – 5
19. On a rural highway, a police officer sees a motorist run a red light at 50 mi/h and begins pursuit. At the
instant the police officer passes through the intersection at 80 mi/h, the motorist is 3 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. In one day the Regal 17 cinema theater made $1590 from 321 people admitted into the movies. The price of
each adult ticket is $6. Children’s tickets are $4.
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.