Question

Solve -3x+2y=-6 -2x+y=6 using substitution

Answer 1

See below

Explanation:

-3x+2y = -6 [1]

-2x + y = 6 [2]

For [1], solve for X.

-3x + 2y = -6

-3x = -6 - 2y

3x = 6 + 2y

x = 2 + (2/3)y

Plug x into [2]

-2(2+(2/3)y) + y = 6

-4 - 4/3y + y= 6

-4/3y + y= 10

-1/3y = 10

y = -30

Answer 2

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Answer:

(x, y) = (-18, -30)

Explanation:

When choosing to solve by substitution, it is convenient if one of the variables has a coefficient of 1 or -1. Here, y has a coefficient of 1 in the second equation, making it easy to rearrange that equation to give an expression for y:

y = 2x +6 . . . . . add 2x to the second equation

Using this expression, we can substitute for y in the first equation:

-3x +2(2x +6) = -6

x + 12 = -6 . . . . . . . . . simplify

x = -18 . . . . . . . . . . . subtract 12

y = 2(-18) +6 = -30 . . . . substitute into the equation for y

The solution is (x, y) = (-18, -30).