5-2 Solving a System of Equations using Substitution
Name _______________
HW: 5.2 pg. 285 #2-7
Guided Notes: Check that each ordered pair is
a solution to a system. If the pair is not a solution,
explain why not.
Example 1: (3, –4)
y = 2x – 10
&
3y = 15 – 9x
Example 2: (2, -6)
y = 2x – 10
Group Problems
You try 1: (2, 3)
y=5–x
&
2y = x +4
&
2y = x +4
You try 2: (4, 1)
&
3y = 15 – 9x
y=5–x
Guided Notes: How to solve an equation when
Group Problems
there are variables on both sides.
Example 3:
2x + 1 = 5x – 9
You try 3:
5x + 10 = 15x – 20
Example 4:
7(x –1)+2 = 3x + 7
You try 4:
4(x –1) – 1 = 2x + 7
Guided Notes: How to solve an equation for a
Group Problems
variable.
Example 5: Solve for x:
Do
x
Undo
=
3x + 6y = 12
Result
You try 5: Solve for x:
Do
x
Undo
=
7x + 14y = 21
Result
Multiply 3
Add 6y
Example 6: Solve for y:
12
50x – 10y = 30
You try 6: Solve for y:
Directed Notes: Solve a system of equations
15x – 5y = 30
Group Problems
using substitution.
Example 7: If both equations are already solved
for the SAME variable, then all you need to do is to
set the equations equal to each other.
y = 2x – 10
You try 7:
y=x+8
y = 20 – 2x
Set equations equal to each other & solve
for x.
y = 5 – 3x
After you have a value for x, solve for y by
substituting your answer for x into the original
equations.
y = 2x – 10
y = 5 – 3x
Solve for y by substituting the value for x
into the original equations.
y=x+8
y = 20 – 2x
Directed Notes: Solve a system of equations
using substitution.
Example 8: Substitute one equation into the other
and solve for x.
y = 5x – 10
2y – 3x = 8
After you have a value for x, solve for y by
substituting your answer for x into the original
equations.
y = 5x – 10
2y – 3x = 8
Directed Notes: Solve a system of equations
using substitution.
Example 9: Solve for one variable first
(solve for y)
5y + 15x = 10
2y + 8x = 8
Group Problems
You try 8: Substitute one equation into the
other and then solve for x.
y = 6 + 3x
3y – 5x = 10
Solve for y by substituting the value for x
into the original equations.
y = 6 + 3x
3y – 5x = 10
Group Problems
Example 9: Solve for one variable first
(solve for x)
6y – 3x = 12
3x + 2y = 12
Then substitute one equation into the other and
solve for x.
2y + 8x = 8
Then substitute one equation into the other
and solve for y.
3x + 2y = 12
After you have a value for x, solve for y by
substituting your answer for x into the original
equations.
5y + 15x = 10
2y + 8x = 8
After you have a value for y, solve for x by
substituting your answer for y into the
original equation.
6y – 3x = 12
3x + 2y = 12