Question

How do solve the following linear system?: `7x+2y=2 , 8x+2y=3`?

Answer 1

The solution is `{(y=-5/2),(x=1):}`

Explanation:

Solve the equations as follows

`{(7x+2y=2),(8x+2y=3):}`

`(2)-(1)`, `=>`, `{(7x+2y=2),(x=1):}`

`<=>`, `{(y=(2-7x)/2),(x=1):}`

`<=>`, `{(y=(2-7)/2),(x=1):}`

`<=>`, `{(y=-5/2),(x=1):}`

Answer 2

See explanation.

Explanation:

The original system is:

`{(7x+2y=2),(8x+2y=3):}`

We can easily notice that `y` has the same coefficient in both equations, so if we multiply any of the equations by `-1` the coefficients will be opposite numbers. I multiplied the first equation and got:

`{(-7x-2y=-2),(8x+2y=3):}`

Now if we add both sides of the equations we get an equation with one variable only (`x`):

`x=1`

Now we have to substitute the calculated value of `x` to calculate `y`:

`8+2y=3`

`2y=-5`

`y=-2.5`

The solution of the system is:

`{(x=1),(y=-2.5):}`