How do you solve the following system?: #-x -2y =-1, 3x -y = -4#

1 Answer
Mar 2, 2018

Answer:

The point of intersection is #(-1,1)#.

Explanation:

Solve system:

#color(blue)("Equation 1:"# #-x-2y=-1#

#color(green)("Equation 2:"# #3x-y=-4#

The given equations are linear equation in standard form. I will show how to solve this system of equations using substitution. The resulting point #(x,y)# is the point of intersection between the lines.

Solve Equation 1 for #x#.

#-x-2y=-1#

Subtract #2y# from both sides of the equation.

#-x=2y-1#

Multiply both sides by #-1#.

#x=-2y+1=#

#x=color(red)(1-2y#

Substitute #color(red)(1-2y# for #x# in Equation 2 and solve for #y#.

#3(color(red)(1-2y))-y=-4#

Expand.

#3-6y-y=-4#

Subtract #3# from both sides.

#-6y-y=-4-3#

Simplify.

#-7y=-7#

Divide both sides by #-7#.

#y=(color(red)cancel(color(black)(-7)))^1/(color(red)cancel(color(black)(-7)))^1#

#y=color(teal)1#

Substitute #color(teal)1# for #y# in Equation 1.

#-x-2(color(teal)(1))=-1#

Simplify.

#-x-2=-1#

Add #2# to both sides.

#-x=-1+2#

Simplify.

#-x=1#

Multiply both sides by #-1#.

#x=-1#

Point of intersection : #(-1,1)#

graph{(-2y-x+1)(-y+3x+4)=0 [-10, 10, -5, 5]}