Solve by Substitution 8x+y=11 , -3x+3y=-21

Problem

{[8*x+y=11],[−3*x+3*y=−21])

Solution

1. Isolate the variable y in the first equation to prepare for substitution.

8*x+y=11

y=11−8*x

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

−3*x+3*(11−8*x)=−21

3. Distribute the constant 3 into the parentheses.

−3*x+33−24*x=−21

4. Combine the like terms involving x

−27*x+33=−21

5. Subtract 33 from both sides of the equation.

−27*x=−54

6. Divide by −27 to solve for x

x=2

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

y=11−8*(2)

y=11−16

y=−5

Final Answer

(x,y)=(2,−5)

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