Algebra 2 – Unit 1 Linear Functions & Inequalities
Name:_______________________________________ Date:______________ Period: ______
1-13 Solving Systems of Equations by Substitution and Elimination
Practice
Solve each system of equations by using substitution.
1. x + y = 20
2. x = -3 – 3y
x = -4 + y
4x + 3y = 6
(
,
)
3. x = 1 + y
2x + 3y = 12
(
,
)
(
,
)
(
,
)
4. 3x + y = 5
y = 2x – 5
(
,
)
6. x − y = -5
3x + 4y = 13
5. 2x + 3y = -4
y=3–x
(
,
)
Algebra 2 – Unit 1 Linear Functions & Inequalities
7. y = 2x
x + y = 12
8. x = 3y - 1
x + 2y = 9
(
,
)
9. y = 2x - 1
4x - y = 10
(
,
)
(
,
)
10. y = -x + 5
x - y = 10
(
,
)
11. What mistake was made in solving the
following system of equations?
y = 3x – 4
3y = 15x + 6
y = 3x – 4
y = 5x + 2
A. Should not have solved for y
Step 1:
Step 2:
Step 3:
Step 4:
3x – 4 = 5x + 2
 4 = 2x + 2
 2 = 2x
1 = x
B. Subtracted incorrectly from Step 2 to Step
3
C. Should have divided by -2 in Step 3
D. Should have added 3x to both sides in Step 1
For problems 12-13, be sure to define your variables.
12. The length of rectangle is twice the width. The perimeter is 18 inches. Find the length and
the width by writing a system of equations and solving them.
13. The width of a rectangle is 4 less than the length. The perimeter is 16 inches. Find the
length and the width by writing a system of equations and solving them.
Algebra 2 – Unit 1 Linear Functions & Inequalities
Solve each system of equations using elimination. Find the solution in the answer column and
write the word next to it in the corresponding box at the bottom of the page. Once you complete
all 12 problems, answer the question asked.
GRAPHED ( 1 , -4 )
1.
5x – 2y = 4
3x + y = 9
ARE ( 2 , 1 )
WILL
HOW
2.
3.
3x – 5y = 13
X – 2y = 5
5.
( -1 , -2 )
INTERSECTION ( 2 , 0 )
7x + 2y = -1
3x – 4y = 19
IF
(2,3)
NO SOLUTION
( -5, 4 )
SOLUTIONS
( 2 , -2 )
LINES
( -2 , 4 )
INFINITELY
( -1 , 3 )
PARALLEL
4.
( -5 , 0 )
x + 2y = 6
5x + 3y = 2
2x + 3y = 7
3x + 4y = 10
(1,4)
BE
( -1 , -1 )
THE
( 1 , -2 )
MANY
(0,3)
INCREASE
( 2 , -4 )
WHO
(1,2)
PERPENDICULAR
(1,3)
6.
THERE
7x – 3y = -5
3x + 2y = 11
DECREASE
(5,2)
( 3 , -2 )
1
2
3
4
5
6
7
8
9
10
11
12
Algebra 2 – Unit 1 Linear Functions & Inequalities
7.
3x-5y = 7
5x – 2y = -1
8.
4x + 3y = 9
3x + 4y = 12
9.
5x – 3y = 16
4x + 5y = -2
10.
4x – 3y = -20
-x – 8y = 5
11.
-3x + 7y = -1
-2x + 5y = 0
12.
5x + 6y = -11
3x + y = -4