This document discusses solving linear systems by substitution. It provides an example of the substitution method showing how to find an equation with a variable alone, rearrange if needed, substitute into the other equation and solve. It then provides two examples of using substitution to solve systems. It concludes with an application example of using a system to solve a word problem about buying turkey and veggie burgers.

1. 4.2 SOLVING
LINEAR SYSTEMS
BY SUBSTITUTION

2. HOW TO USE SUBSTITUTION
1.
Find equation Example:
with a variable y = 2x – 4
alone.
7x – 2y = 5

2.
3.
Rearrange if
needed.
Substitute and
solve.
Plug in answer
and solve for
other variable.

3. EXAMPLE:
Solve
using substitution.
y = 2x + 3
y = 5x

4. EXAMPLE:
Solve
using substitution.
x + 4y = 14
3x + 7y = 22

5. YOU TRY!
Solve
using substitution.
4x + 2y = 0
y=½x–5

6. APPLICATIONS
Example
1:
You buy a total of 50 turkey and veggie
burgers for $90. You pay $2 per turkey
burger and $1.50 per veggie burger.
Write and solve a system to find the
number x of turkey burgers and y veggie
burgers you buy.

7. Write
a verbal model:
Write
system of equations:

8. Solve:
x + y = 50
2x + 1.5y = 90

9. YOU TRY!
A
juice stand sells lemonade for $2
per cup and orange juice for $3 per
cup. The stand sells a total of 100
cups of juice for $240. Write and
solve a system to find the number
of lemonade and orange juice cups
sold.