SOLUTION: How to slove {y=-x+3}{y=3/2x-2}

Question 106351This question is from textbook Algebra 2
: How to slove {y=-x+3}{y=3/2x-2}
This question is from textbook Algebra 2

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
This is a system of two linear equations in two variables. There are a number of different ways to solve this, either using determinants, substitution, or by adding and subtracting the equations to eliminate one of the variables. Since the coefficient on one of the variables (y in this case) is 1 in both equations, term by term subtraction of the two equations eliminates the y variable immediately -- therefore that is the method I'll demonstrate here.
1) y = -x + 3
2) y = (3/2)x - 2
Arrange the equations so that the variables are on one side of the '=' sign, and the constants on the other, thus:
1) y + x = 3
2) y -(3/2)x = -2
To subtract the two equations, change the signs on all terms of eq. 2) and add them, term by term, thus:
1) y + x = 3
2) -y +(3/2)x = 2
-----------------
3) 0 +(5/2)x = 5
Now solve the resulting equation [3)] for x, thus:
(5/2)x = 5
5x = 10
x = 2
Now that we have a value for x, we can solve either of the given equations for y.
y + 2 = 3
y = 1
Let's check our answers:
1) 1 = -2 + 3 (check)
2) 1 = (3/2)*2 - 2, 1 = 3 - 2 (check)

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