4x + 6y = -5
8x = 12y - 10
solve the system

x = -5/4, y = 0

Step-by-step explanation:

Solve the following system:

{4 x + 6 y = -5 | (equation 1)

{8 x = 12 y - 10 | (equation 2)

Express the system in standard form:

{4 x + 6 y = -5 | (equation 1)

{8 x - 12 y = -10 | (equation 2)

Swap equation 1 with equation 2:

{8 x - 12 y = -10 | (equation 1)

{4 x + 6 y = -5 | (equation 2)

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

{8 x - 12 y = -10 | (equation 1)

{0 x+12 y = 0 | (equation 2)

Divide equation 1 by 2:

{4 x - 6 y = -5 | (equation 1)

{0 x+12 y = 0 | (equation 2)

Divide equation 2 by 12:

{4 x - 6 y = -5 | (equation 1)

{0 x+y = 0 | (equation 2)

Add 6 × (equation 2) to equation 1:

{4 x+0 y = -5 | (equation 1)

{0 x+y = 0 | (equation 2)

Divide equation 1 by 4:

{x+0 y = (-5)/4 | (equation 1)

{0 x+y = 0 | (equation 2)

Collect results:

 {x = -5/4, y = 0