Solve by Substitution y=6x-11 , -2x-3y=-7

Problem

{[y=6*x−11],[−2*x−3*y=−7])

Solution

1. Identify the expression for y from the first equation, which is y=6*x−11

2. Substitute this expression for y into the second equation to create an equation with only one variable.

−2*x−3*(6*x−11)=−7

3. Distribute the −3 into the parentheses.

−2*x−18*x+33=−7

4. Combine the like terms on the left side of the equation.

−20*x+33=−7

5. Isolate the term with x by subtracting 33 from both sides.

−20*x=−40

6. Solve for x by dividing both sides by −20

x=2

7. Substitute the value x=2 back into the first equation to find the value of y

y=6*(2)−11

8. Simplify the expression to find y

y=12−11

y=1

Final Answer

(x,y)=(2,1)

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