Solve by Substitution x-6y=-13 , 5y-4x=14

Problem

{[x−6*y=−13],[5*y−4*x=14])

Solution

1. Isolate the variable x in the first equation by adding 6*y to both sides.

x=6*y−13

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

5*y−4*(6*y−13)=14

3. Distribute the −4 into the parentheses.

5*y−24*y+52=14

4. Combine the y terms and subtract 52 from both sides to isolate the term with y

−19*y=−38

5. Divide by −19 to find the value of y

y=2

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

x=6*(2)−13

7. Simplify the expression to find the value of x

x=12−13

x=−1

Final Answer

(x,y)=(−1,2)

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