Question 927554: How do I find X and Y by using substitution?
2x + y = 0
x - 3y = -7
Answer by Techpriest(29)   (Show Source):
You can put this solution on YOUR website! Well, you see you would need to use substitution, you can find either the x-value or y-value preferring your choice. In order to find that, we must find the x-value or y-value through equality properties for the first equation:
2x + y = 0
2x - 2x + y = 0 - 2x Subtraction Property of Equality
y = -2x Simplify
OR
2x + y = 0
2x + y - y = 0 - y Subtraction Property of Equality
2x = -y Simplify
2x/2 = -y/2 Division Property of Equality
x = -y/2 Simplify
Or we can do the same for the second equation:
x - 3y = -7
x - x - 3y = -7 - x Subtraction Property of Equality
-3y = -7 - x Simplify
-3y/-3 = (-7 - x)/-3 Division Property of Equality
y = (-7 - x)/-3 Simplify
OR
x - 3y = -7
x - 3y + 3y = -7 + 3y Addition Property of Equality
x = -7 + 3y Simplify
You may choose whichever is easier for you. After finding the x-value or y-value, you must substitute them in. I will substitute my first example for the easiness in for the second equation as the first example will always be true for the first equation.
y = -2x
x - 3y = -7
x - 3(-2x) = -7
x + 6x = -7
7x = -7
x = -1
Now, if we plug in x for the y-value, we will find out that:
x = -1
y = -2x
y = -2(-1)
y = 2
x = -1, y = 2
If we plug in the x-value and y-value for both of those equation, they will be true, which gives you your answer!
2x + y = 0
2(-1) + -2 = 0 Substitution!
2 + -2 = 0 Simplify
0 = 0
x - 3y = -7
-1 - 3(2) = -7 Substitution
-1 - 6 = -7 Simplify
-7 = -7 Combine like terms.
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