Problem #1
Solve the following system by graphing. Type your solution in the space provided.
x + y = 3
3x - 2y = 4
The solution is the point: ( ), ( )
Answer: (2, 1)
Problem #2
Solve the following system by substitution.
x + 3y = 4
6y + 2x = 12
The solution is the point: ( ), ( )
Answer: No solution
x = -3y + 4
6y + 2(-3y + 4) = 12
6y - 6y + 8 = 12
8 = 12
When you end up with an equation that is not true, there are no solutions!
Problem #3
Solve the following system by substitution.
2x + 7y = 8
3x + 5y = 1
The solution is the point: ( ), ( )
Answer: (-3, 2)
3(2x + 7y = 8)
-2(3x + 5y = 1)
6x + 21y = 24
-6x - 10y = -2
11y = 22
y = 2
Then, subtitute in the y value:
-2x + 7y = 8
-2x + 7(2) = 8
-2x + 14 = 8
-2x = -6
x = -3
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