Solve system of equations:

These are linear equations in standard form #(Ax+By=C)#, and can be solved by substitution. The resulting #x# and #y# values represent the intersection of the two lines on a graph.

#color(red)("Equation 1":# #x-2y=8#

#color(blue)("Equation 2":# #2x+3y=9#

I'm going to start with the #color(red)("Equation 1"# and solve for #x#, because its the simplest equation.

Subtract #8+2y# from both sides.

#x=8+2y#

Now solve for #y# in #color(blue)("Equation 2"# by substituting #8+2y# for #x#.

#2(8+2y)+3y=9#

Expand.

#16+4y+3y=9#

Subtract #16# from both sides.

#4y+3y=9-16#

Simplify.

#7y=-7#

Divide both sides by #7#.

#y=(-7)/7#

#y=color(blue)(-1)#

Now substitute #-1# for #y# in #color(red)("Equation 1"# and solve for #x#.

#x-2(-1)=8#

Simplify.

#x+2=8#

Subtract #2# from both sides.

#x=8-2#

#x=color(red)6#

The point of intersection is: #(color(red)6,color(blue)(-1))#