Solve by Substitution x-3y=8 , -2x+3y=-7

Problem

{[x−3*y=8],[−2*x+3*y=−7])

Solution

1. Isolate the variable x in the first equation by adding 3*y to both sides.

x=3*y+8

2. Substitute the expression for x into the second equation.

−2*(3*y+8)+3*y=−7

3. Distribute the −2 through the parentheses.

−6*y−16+3*y=−7

4. Combine the y terms on the left side.

−3*y−16=−7

5. Isolate the y term by adding 16 to both sides.

−3*y=9

6. Solve for y by dividing both sides by −3

y=−3

7. Substitute the value of y back into the isolated equation for x

x=3*(−3)+8

8. Simplify to find the value of x

x=−9+8

x=−1

Final Answer

(x,y)=(−1,−3)

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