Question

Solve this system of equations 3x-5y=7 4x+10y=16

Answer 1

Solve the following system:
{3 x - 5 y = 7 | (equation 1)
{10 y - 4 x = 16 | (equation 2)


Swap equation 1 with equation 2:
{-(4 x) + 10 y = 16 | (equation 1)
{3 x - 5 y = 7 | (equation 2)

Add 3/4 × (equation 1) to equation 2:
{-(4 x) + 10 y = 16 | (equation 1)
{0 x+(5 y)/2 = 19 | (equation 2)


Divide equation 1 by 2:
{-(2 x) + 5 y = 8 | (equation 1)
{0 x+(5 y)/2 = 19 | (equation 2)


Multiply equation 2 by 2:
{-(2 x) + 5 y = 8 | (equation 1)
{0 x+5 y = 38 | (equation 2)

Divide equation 2 by 5:
{-(2 x) + 5 y = 8 | (equation 1)
{0 x+y = 38/5 | (equation 2)

Subtract 5 × (equation 2) from equation 1:
{-(2 x)+0 y = -30 | (equation 1)
{0 x+y = 38/5 | (equation 2)

Divide equation 1 by -2:
{x+0 y = 15 | (equation 1)
{0 x+y = 38/5 | (equation 2)
Collect results:
Answer:  {x = 15
                {y = 38/5 or 7.6 decimal