How do you solve #x + 4y = -1# and #2x - y = 7#?

1 Answer
Mar 9, 2018

Answer:

The lines intersect at the point #(3,-1)#.

Refer to the explanation for the process.

Explanation:

Solve system of equations

Equation 1: #x+4y=-1#

Equation 2: #2x-y=7#

Both equations are linear equations in standard form:

#Ax+By=C#.

The point #(x,y)# which results from solving the system is the point of intersection between the two lines.

I will use the substitution method to solve the system.

Solve Equation 1 for #x#.

#x+4y=-1#

Subtract #4y# from both sides of the equation.

#x=-4y-1#

Substitute #-4y-1# for #y# in Equation 2.

#2x-y=7#

#2(-4y-1)-y=7#

Expand.

#-8y-2-y=7#

Add #2# to both sides.

#-8y-y=7+2#

Simplify.

#-9y=9#

Divide both sides by #-9#.

#y=9/(-9)#

Simplify.

#y=-1#

To solve for #x#, substitute #-1# for #y# in Equation 1.

#x+4y=-1#

#x+4(-1)=-1#

Simplify.

#x-4=-1#

Add #4# to both sides.

#x=-1+4#

#x=3#

The point of intersection between the two lines is #(3,-1)#.

graph{(4y+x+1)(-y+2x-7)=0 [-10, 10, -5, 5]}