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))#
