How do you solve the following system of equations?: x+y= -2 , x-2y=13?

2 Answers
Mar 23, 2018

x = 3
y = -5

Explanation:

since we have two unknowns we need minimum of two equations to solve for them , and we have that too

lets see the first equation
x+y =-2
the first objective is to write either x in terms of y or y in terms of x
so i add -y to both sides , and we get
x = -2-y
take this value of x and plug it in equation 2
so
this x-2y=13
becomes
(-2-y)-2y =13
solve for y to get a value
-2 -3y = 13
-3y = 15
-y = 5
or
y = -5
since we got y value , we can plug it back in the first equation to get x value
x + (-5) = -2 or x = 5-2 = 3
So , x=3 , y=-5

Mar 23, 2018

x = 3
y = -5

Explanation:

You add/subtract the two equations with each other, using the = sign as a point of reference:

x+y = -2

would be the first equation. We can label it as equation (1)

x-2y = 13

would be the second equation. We can label it as equation (2)

Now, we can subtract equation (2) from equation (1) [the idea here is to leave us with only one variable, that way we can solve the equation as usual]

(1) - (2) would be

x-x + y-(-2y) = -2-13

0 + 3y = -15

so

y = -5

Now we can take y and use it in equation (1);

x+(-5) = -2

x = 3

So

x = 3 and y = -5