Substitution Method
Easy
1.
2x+y=3
3x-2y=8
Solution
Solve the first equation for y because it has a coefficient of 1
2x+y=3
y=3-2x
This equation has only one
Substitute 3-2x for y in the second equation.
variable
3x-2y=8
3x-2(3-2x)=8
3x- 6 + 4x=8
Use the distributive
property
7x=14
x=2
Substitute 2 for x in either original equation to find y.
First equation:
2x + y=3
Second equation:
2(2)+y=3
3(2)-2y=8
y=-1
-2y=8-6
3x – 2y=8
y=-1
Solution is (2,-1)
Check
2x+y=3

Always check your answer both
by substituting them into both
2(2)+(-1)=3 original equations
True
3x-2y=8
3(2)-2(-1)=8
Medium
3.
X
10%
6%
Y
=
500
mL
4%
True
Solution
Write two equations in
x and y. let x and y represent the amounts of the
10% and 4% solutions, respectively.
amount of
amount of
amount
of
+
=
6% solution
10% solution
x
4% solution
+
y
=
500
saline in
saline in
saline in
10% solution
+
4% solution
=
6%
solution
0.10x
+
0.04y
=
0.06(500)
Solve the first equation for y.
x+y=500
y=500-x
The first equation can
be solved for either x
or y.
Substitute 500-x for y into the second equation, and solve for x
0.10x+0.04y=0.06(500)
0.10x+0.04(500-x)=0.06(500)
Substitute
0.10x+20-0.04x=30
Simplify
0.06x=10
x167
Substitute 167 for x into the first equation.
x + y = 500
167 + y  500
y  333
Hard
5.
x+y+z=5
2x-3y+z=-2
4z=8
Solution
Solve the third equation for z.
4z=8
z=2
Substitute 2 for z in the first and second equations. Then simplify.
x+y+z=5
x+y+2=5
x+y=3
2x-3y+z=-2

2x-3y+2=-2

2x-3y=-4
z=2
Use substitution to solve the resulting system. x+y=3
2x-3y=-4
Substitute 3-x
for y in 2x- 3y=-4
x+y=3
2x-3y=-4
y=3-x

2x-3( 3-x) = -4
2x-9=3x=-4
5x=5
x=1
Now substitute 1 for x and 2 for z to find y.
x+y+z=5
You can use either the first
1+y+2=5
or second equation of the
y=2
original system.
Solution is (1,2,2)
Check
x+y+z=5
2x-3y+z=-2
4z=8

1+2+2=5
2(1)-3(2)+2=-2
4(2)=8
True
True
True