Solve by Substitution x+2y=-1 , 3x+5y=-6

Problem

{[x+2*y=−1],[3*x+5*y=−6])

Solution

1. Isolate the variable x in the first equation by subtracting 2*y from both sides.

x=−1−2*y

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

3*(−1−2*y)+5*y=−6

3. Distribute the 3 into the parentheses.

−3−6*y+5*y=−6

4. Combine the y terms on the left side.

−3−y=−6

5. Solve for y by adding 3 to both sides and then multiplying by −1

−y=−3

y=3

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

x=−1−2*(3)

7. Simplify to find the value of x

x=−1−6

x=−7

Final Answer

(x,y)=(−7,3)

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