Question

Solve the system of linear equations. separate the x- and y- values with a coma.

7x-3y=37
14x+11y=23

Answer 1

Solve the following system:

{7 x - 3 y = 37 | (equation 1)

{14 x + 11 y = 23 | (equation 2)

Swap equation 1 with equation 2:

{14 x + 11 y = 23 | (equation 1)

{7 x - 3 y = 37 | (equation 2)

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

{14 x + 11 y = 23 | (equation 1)

{0 x - (17 y)/2 = 51/2 | (equation 2)

Multiply equation 2 by 2/17:

{14 x + 11 y = 23 | (equation 1)

{0 x - y = 3 | (equation 2)

Multiply equation 2 by -1:

{14 x + 11 y = 23 | (equation 1)

{0 x+y = -3 | (equation 2)

Subtract 11 × (equation 2) from equation 1:

{14 x+0 y = 56 | (equation 1)

{0 x+y = -3 | (equation 2)

Divide equation 1 by 14:

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

{0 x+y = -3 | (equation 2)

Collect results:

Answer: {x = 4

{y = -3

Answer 2

Solve the following system:
{7 x - 3 y = 37 | (equation 1)
{14 x + 11 y = 23 | (equation 2)
Swap equation 1 with equation 2:
{14 x + 11 y = 23 | (equation 1)
{7 x - 3 y = 37 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{14 x + 11 y = 23 | (equation 1)
{0 x - (17 y)/2 = 51/2 | (equation 2)

Multiply equation 2 by 2/17:
{14 x + 11 y = 23 | (equation 1)
{0 x - y = 3 | (equation 2)

Multiply equation 2 by -1:
{14 x + 11 y = 23 | (equation 1)
{0 x+y = -3 | (equation 2)
Subtract 11 × (equation 2) from equation 1:
{14 x+0 y = 56 | (equation 1)
{0 x+y = -3 | (equation 2)

Divide equation 1 by 14:
{x+0 y = 4 | (equation 1)
{0 x+y = -3 | (equation 2)
Collect results:
Answer: {x = 4
{y = -3