How do you solve the system of equations $x-y=7$ and $-2x+5y=-8$ ?

Shelia Lawrence
2021-12-25
Answered

How do you solve the system of equations $x-y=7$ and $-2x+5y=-8$ ?

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Terry Ray

Answered 2021-12-26
Author has **50** answers

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:

$2x-2y=14$

$\pm 2x+5y=-8$

$3y=6$

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

Then we simply add that to the second equation:

The positive 2x and the negative 2x cancel out, leaving us with just the

Divide both sides by 3 and we get

Last, just plug 2 in for y in either equation (Ill

Charles Benedict

Answered 2021-12-27
Author has **32** answers

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

$2\cdot (x-y=7)=2x-2y=14\to$ 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.

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

Now plug in the 2 for y in the first equation to solve for x

We have now solved both variables. Check to make sure both equations are equal.

karton

Answered 2021-12-30
Author has **368** answers

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

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