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

3 Answers
Aug 7, 2017

By manipulating the first equation and combining it with the second, we can eventually arrive at the answer: x = 9, y = 2.

Explanation:

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 (I'll choose the first since it's simpler):

x-2=7

Add 2 to both sides to get x=9.

So our final answer is x = 9, y = 2.

Aug 7, 2017

You will need to solve one of the variables using the substitution method.

Explanation:

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 x variable

2 * ( x - y = 7) = 2x - 2y = 14 -> 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.

Aug 7, 2017

The point of intersection between the two lines is (9,2).

Refer to the explanation for the process.

Explanation:

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=7color(white)(...)andcolor(white)(...)-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+y for x in the 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 first equation and solve for x.

x-2=7

Add 2 to both sides.

x=9

The point of intersection is (9,2).

https://www.wolframalpha.com/input/?i=solve+system:+x-y%3D7,+-2x%2B5y%3D-8&wal=header