Solve the system y=2x-6; y=-1/2x+4

x = 108/5, y = 186/5

Step-by-step explanation:

Solve the following system:

{y = 2 x - 6 | (equation 1)

y = 48 - x/2 | (equation 2)

Express the system in standard form:

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

x/2 + y = 48 | (equation 2)

Add 1/4 * (equation 1) to equation 2:

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

0 x + (5 y) / 4 = 93/2 | (equation 2)

Multiply equation 2 by 4:

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

0 x+5 y = 186 | (equation 2)

Divide equation 2 by 5:

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

0 x+y = 186/5 | (equation 2)

Subtract equation 2 from equation 1:

{ - (2 x) + 0 y = (-216) / 5 | (equation 1)

0 x+y = 186/5 | (equation 2)

Divide equation 1 by - 2:

{x+0 y = 108/5 | (equation 1)

0 x+y = 186/5 | (equation 2)

Collect results:

Answer: {x = 108/5, y = 186/5