How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #3x - 2y = 10# and #5x + 2y = 6#?

1 Answer
Jul 19, 2018

Answer:

The lines intersect at a single point, therefore the system of equations is consistent.

Explanation:

Equation 1: #3x-2y=10#

Equation 2 : #5x+2y=6#

Both equations are in the standard form for a linear equation. This form makes it easy to determine the x- and y-intercepts. We can use those two points to graph each equation.

X-intercept: value of #x# when #y=0#

Substitute #0# for #y# and solve for #x#.

Y-intercept: value of #y# when #x=0#

Substitute #0# for #x# and solve for #y#.

Equation 1

#3x-2y=10#

X-intercept: Substitute #0# for #y# and solve for #x#.

#3x-2(0)=10#

#3x=10#

Divide both sides by #3#.

#x=10/3# or #~~3.333#

x-intercept: #(10/3,0)# or #(~~3.333,0)# Plot this point.

Y-intercept: Substitute #0# for #x# and solve for #y#.

#3(0)-2y=10#

#-2y=10#

Divide both sides by #-2#.

#y=10/(-2)#

#y=-5#

y-intercept: #(0,-5)# Plot this point.

Draw a straight line through the two points. This is the graph for Equation 1.

Equation 2

#5x+2y=6#

X-intercept: Substitute #0# for #y# and solve for #x#.

#5x+2(0)=6#

#5x=6#

Divide both sides by #5#.

#x=6/5# or #1.2#

x-intercept: #(6/5,0)# or #(1.2,0)# Plot this point.

Y-intercept: Substitute #0# for #x# and solve for #y#.

#5(0) + 2y=6#

#2y=6#

Divide both sides by #2#.

#y=6/2#

#y=3#

y-intercept: #(0,3)# Plot this point.

Draw a line between the two points. This is the graph of Equation 2.

The lines intersect at a single point, therefore the system of equations is consistent.

graph{(3x-2y-10)(5x+2y-6)=0 [-10, 10, -5, 5]}