What is x in the following equation
y=3x-5
6x+3y=15

x = 2 , y = 1

Step-by-step explanation:

Solve the following system:

{y = 3 x - 5 | (equation 1)

3 y + 6 x = 15 | (equation 2)

Express the system in standard form:

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

6 x + 3 y = 15 | (equation 2)

Swap equation 1 with equation 2:

{6 x + 3 y = 15 | (equation 1)

-(3 x) + y = -5 | (equation 2)

Add 1/2 × (equation 1) to equation 2:

{6 x + 3 y = 15 | (equation 1)

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

Divide equation 1 by 3:

{2 x + y = 5 | (equation 1)

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

Multiply equation 2 by 2/5:

{2 x + y = 5 | (equation 1)

0 x+y = 1 | (equation 2)

Subtract equation 2 from equation 1:

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

0 x+y = 1 | (equation 2)

Divide equation 1 by 2:

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

0 x+y = 1 | (equation 2)

Collect results:

{x = 2 , y = 1