Solve by Substitution 2x-5y=6 , -2x+10y=-16

Problem

{[2*x−5*y=6],[−2*x+10*y=−16])

Solution

1. Isolate the term 2*x in the first equation.

2*x=5*y+6

2. Solve for x by dividing both sides by 2

x=(5*y+6)/2

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

−2*((5*y+6)/2)+10*y=−16

4. Simplify the equation by canceling the factor of 2

−(5*y+6)+10*y=−16

5. Distribute the negative sign and combine like terms.

−5*y−6+10*y=−16

5*y−6=−16

6. Solve for y by adding 6 to both sides and dividing by 5

5*y=−10

y=−2

7. Substitute the value of y back into the expression for x

x=(5*(−2)+6)/2

x=(−10+6)/2

x=(−4)/2

x=−2

Final Answer

(x,y)=(−2,−2)

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