Algebra 1 300 Name____________________

Systems Quiz Review Date__________

SYSTEMS QUIZ REVIEW

Topics to Study:

• Linear Systems

o Two linear equations. . .we are interested in if and where they intersect.

o If the lines intersect, then there is only ONE solution.

o If the lines are parallel, then there is NO solution.

o If the lines are the same, then there are an INFINITE # of solutions.

• Graphing Method

o Write each equation in slope intercept form and graph the lines.

o The solution is where they intersect.

• Substitution Method

o Transform one equation for one variable and then plug it into the other

equation.

o Solve and then find the other variable.

• Elimination

o Find one variable that has the same coefficients and then add/subtract the

equations.

o If the variables do not have the same coefficients then multiply the equations

by a number that will make them equal. Then add/subtract.

*****Always check your answers by PLUGGING POINT BACK INTO BOTH

ORIGINAL EQUATIONS!

Algebra 1 300 Name____________________

Systems Quiz Review Date__________

Part I: Solve the systems by the graphing method.

1. 4

3 2

y x

y x

2.

1

5 7

x y

x y

3. 4 2 6

3

x y

x y

4.

2 4

7

y x

y

Algebra 1 300 Name____________________

Systems Quiz Review Date__________

Part II: Solve by the substitution method.

5. 3

5 16

x y

x y

6.

8 3

4 5 15

x y

x y

7. 9 2 6

3 12

p q

p q

8.

6 4 5

9 6 8

x y

x y

9. 3

2𝑥 + 𝑦 = −5 10. −𝑥 + 3𝑦 = −10

3𝑥 + 2𝑦 = −10 −3𝑥 + 2𝑦 = −27

Algebra 1 300 Name____________________

Systems Quiz Review Date__________

Part III: Solve by the elimination method.

11. 2 3 1

3 4

a b

a b

12.

5 9 3

4 3 6

x y

x y

13. 2 3 1 0

3 5 2 0

p q

p q

14.

5 11

4 2

33

x y

yx

15.

18 10

3

520 25

6

a b

a b

16. 5y = -7x - 7

8 = 6y – 8x

Algebra 1 300 Name____________________

Systems Quiz Review Date__________

Part III: Solve by your favorite method.

17. 2𝑥 + 3𝑦 = 19 18. 2𝑥 − 2𝑦 = 0

−4𝑥 − 𝑦 = −8 3𝑦 = −8𝑥 + 10