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

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.

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.

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##color(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)#.