Find the solution to the system of equations given below using elimination by addition. 10x + 10y = 60 5x - 5y = 40

x = 7 ,  y = -1

Step-by-step explanation by elimination:

Solve the following system:

{10 x + 10 y = 60 | (equation 1)

5 x - 5 y = 40 | (equation 2)

Subtract 1/2 × (equation 1) from equation 2:

{10 x + 10 y = 60 | (equation 1)

0 x - 10 y = 10 | (equation 2)

Divide equation 1 by 10:

{x + y = 6 | (equation 1)

0 x - 10 y = 10 | (equation 2)

Divide equation 2 by 10:

{x + y = 6 | (equation 1)

0 x - y = 1 | (equation 2)

Multiply equation 2 by -1:

{x + y = 6 | (equation 1)

0 x+y = -1 | (equation 2)

Subtract equation 2 from equation 1:

{x+0 y = 7 | (equation 1)

0 x+y = -1 | (equation 2)

Collect results:

 {x = 7 ,  y = -1

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!