Solve by Substitution -5x+y=-12 , -10x+5y=-15

Problem

{[−5*x+y=−12],[−10*x+5*y=−15])

Solution

1. Isolate the variable y in the first equation.

−5*x+y=−12

y=5*x−12

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

−10*x+5*(5*x−12)=−15

3. Distribute the constant 5 into the parentheses.

−10*x+25*x−60=−15

4. Combine like terms on the left side.

15*x−60=−15

5. Solve for x by adding 60 to both sides and then dividing by 15

15*x=45

x=3

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

y=5*(3)−12

y=15−12

y=3

Final Answer

(x,y)=(3,3)

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