# How do you solve the system of equations x-y=7 and

How do you solve the system of equations $x-y=7$ and $-2x+5y=-8$ ?
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Terry Ray
Your goal here is to remove one of the variables from the problem. You can see that the first equation has x and the second equation has -2x. If we double the first equation, we get:
$2x-2y=14$
Then we simply add that to the second equation:
$2x-2y=14$
$±2x+5y=-8$
$3y=6$
The positive 2x and the negative 2x cancel out, leaving us with just the $3y=6$.
Divide both sides by 3 and we get $y=2$
Last, just plug 2 in for y in either equation (Ill
###### Not exactly what you’re looking for?
Charles Benedict
Begin by solving either the x or y variable by first eliminating or canceling out one of the variables. We can then plug in that variable into the first equation and solve for the second equation
$x-y=7$ and $-2x+5y=-8$
To Solve for y in the second equation, start by multiplying the first equation by 2 and add the result to second in order to cancel out the
$2\cdot \left(x-y=7\right)=2x-2y=14\to$ Add this to the second equation
$-2x+5y=-8$
$+2x-2y=14$
$3y=6$
$y=2$
Now plug in the 2 for y in the first equation to solve for x
$x-2+2=7+2$
$x=9$
We have now solved both variables. Check to make sure both equations are equal.
###### Not exactly what you’re looking for?
karton
Solve system of equations: These are linear equations. Since they are a system, both equations are solved simultaneously by substitution. The resulting values for x and y is the point at which the two lines intersect on a graph. The two equations are: x-y=7 and -2x+5y=-8 First Equation: x-y=7 x-y=7 Add y to both sides. x=7+y Second Equation: -2x+5y=-8 Substitute 7+yfor x in equation. -2(7+y)+5y=-8 Simplify. -14-2y+5y=-8 Add 14 to both sides. 2y+5y=-8+14 Simplify. 3y=6 Divide both sides by 3. y=2 Now substitute the value of y back into the firs equation and solve for x. x-2=7 Add 2 to both sides. x=9