How do you write the the ordered pair that is the solution to the following system of equations: #-3x + y = 4# and #-7x + y = 12?#

2 Answers
Jan 5, 2018

Answer:

Solve for one variable and substitute

Explanation:

Subtract the two equations from each other to eliminate the 'y' variable.
#(-3x+y=4)# #-#
#color(white)(..........................)# #larr# Subtracting a (-) by a (-) gives a (+).
#(-7x+y=12)#

#4x = -8#

#x =-2#

Plug in #-2# into one of the two equations to solve for #y#.

#-3(-2)+y=4#

#y=-2#

The solution is #(-2,-2)#

Jan 5, 2018

Answer:

The point of intersection is #(-2,-2)#.

Explanation:

Given:

Equation 1: #-3x+y=4#

Equation 1: #-7x+y=12#

I will use substitution to solve this system of equations. The ordered pair that is the solution is the point at which the two lines intersect.

Solve Equation 1 for #y#.

#-3x+y=4#

Add #3x# to both sides and simplify.

#y=3x+4#

Substitute #3x+4# for #y# in Equation 2 an d solve for #x#.

#-7x+y=12#

#-7x+3x+4=12#

Simplify.

#-4x+4=12#

Subtract #4# from both sides.

#-4x=12-4#

Simplify.

#-4x=8#

Divide both sides by #-4#.

#x=8/(-4)#

Simplify.

#x=-2#

Substitute #-2# for #x# in Equation 1 and solve for #y#.

#-3x+y=4#

#-3(-2)+y=4# #larr# Two negatives make a positive.

Simplify.

#6+y=4#

Subtract #6# from both sides.

#y=4-6#

#y=-2#

Point of Intersection: #(-2,-2)#

graph{(y-3x-4)(y-7x-12)=0 [-11.25, 11.25, -5.625, 5.625]}