Question

type the ordered pair that is the solution to these equations.

2x+5y=-9
3x-4y=-2

Answer 1

To solve a system of linear equations like this one, you can use several methods.
One of the methods is elimination. In elimination, you need to add both equations and eliminate one variable. This is very simple if the system of equations were, for example,
x + y = 5
x - y = 1
Since you have y in one equation and -y in the other equation, simply adding them will eliminate the y's and you get
2x = 6
x = 3.

In our case, if you add the two equations, no variable will be eliminated, so we need an extra step. That extra step is to multiply one or both equations by numbers to make a variable get eliminated with addition.
Since in this problem's system of equations you have 5y and -4y, if you multiply the first equatoin by 4, the y term will become 20y. If you multiply the second equation by 5, the y term will become -20y which when added together will eliminate y.
Let's do that. Let's multiply the entire first equation by 4 and below it, we'll write the entire second equatuion multiplied by 5:
8x + 20y = -36
15x - 20y = -10
------------------ (add)
23x = -46
Divide both sides by 23:
x = -2
Now that we have x, we simply replace it in one of the two original equations.
Let's use the first equation:
2x + 5y = -9, but x = -2, so
2(-2) + 5y = -9
-4 + 5y = -9
Add 4 to both sides:
5y = -5
Divide both sides by 5:
y = -1

To check, substitute x = -2and y = -1in _both_ equations and make sure those values of x and y work in both equations.

Solution: (-2, -1)