Question

How do you solve the system of equations `\frac { 3} { 5} x + y = \frac { 23} { 25}` and `\frac { 1} { 5} x - y = \frac { 1} { 25}`?

Answer 1

`x = 6/5` and `y = 5/25`

Explanation:

Step 1) Solve the first equation for `y` while keeping the equation balanced:

`3/5 x + y -3/5 x = 23/25 - 3/5 x`

`y = 23/25 - 3/5 x`

Step 2) Substitute `23/25 - 3/5 x` for `y` in the second equation and solve for `x`:

`1/5 x - (23/25 -3/5 x) = 1/25`

`1/5 x - 23/25 + 3/5 x = 1/25`

`4/5 x - 23/25 = 1/25`

`4/5 x - 23/25 + 23/25 = 1/25 + 23/25`

`4/5x = 24/25`

`5/4 * 4/5 x = 5/4 * 24/25`

`x = 6/5`

Step 3) Substitute `8/5` for `x` in the solution for the first equation and calculate `y`:

`y = 23/25 - 3/5*6/5`

`y = 23/25 - 18/25`

`y = 5/25`