Systems of Equations
Learn how to solve two equations at the same time.
What You’ll Learn:
-
Substitution -
Elimination -
Graphing solutions
Lesson 1:
Substitution
Example:
y = x + 2
2x + y = 8
2x + (x + 2) = 8
3x + 2 = 8
x = 2
2x + y = 8
4 + y = 8
y = 4
(2, 4)
Lesson 2:
Elimination
Add/or subtract to eliminate variable.
Example: Add or subtract to eliminate variable
2x + 2y = 10
x-2y= 2
3x + 0y = 12
3x= 12
x = 4
Substitute 4
2(4) + 2y = 10
8 + 2y = 10
2y = 2
y = 1
Practice Problems
Easy
y = x + 1
x + y = 7
Medium
3x + 2y = 4
2x + 3y = 1
Challenge
Two friends spent a total of $30 on lunch. One spent $6 more than the other. How much did each person spend?
Common Mistakes to Avoid
-
Arithmetic errors -
Incorrect substitution -
Losing track of variables
Quick Recap:
Solution = the (x, y)
that works in
BOTH equations
The point where the two lines intersect.
Answer Key:
Easy:
(3, 4)
Medium:
(2, -1)
Challenge:
One friend spent $18, the other spent $12
Next:
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