Question

What is the solution to the systen of equations y=1/2x+2 and y=-2x-3

Answer 1

For this case we must solve a system of two equations with two unknowns, given by "x" and "y".

We have:

`y = \frac {1} {2} x + 2 (1)\\y = -2x-3 (2)`

We multiply (2) by -1:

`-y = 2x + 3 (3)`

We add (1) and (3):

`y-y = \frac {1} {2} x + 2x + 2 + 3\\0 = \frac {5} {2} x + 5\\-5 = \frac {5} {2} x`

Clearing x:

`-10 = 5x\\x = \frac {-10} {5}\\x = -2`

We substitute
`x = -2` in (2)

`y = -2 (-2) -3\\y = 4-3\\y = 1`

Thus, the solution of the system is
`(x, y) = (- 2,1)`

Answer:

the solution of the system is
`(x, y) = (- 2,1)`