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$(x, y) = (- 2,1)$