How do you solve #2x+3y=6# and #2x-y=-2# using substitution?

1 Answer
Apr 5, 2017

Answer:

#(0,2)#

Explanation:

To solve by #color(blue)"substitution"#

Rearrange one of the equations in terms of x or y then substitute into the other equation and solve for x or y

#2x-y=-2to(1)#

#2x+3y=6to(2)#

Rearrange ( 1 ) to obtain y in terms of x , avoiding the use of fractions.

#rArry=2x+2to(3)#

#color(blue)"Substitute "# into equation ( 2 )

#2x+3(color(red)(2x+2))=6larrcolor(red)" and solve for x"#

#rArr2x+6x+6=6#

#rArr8x+6=6#

subtract 6 from both sides.

#8xcancel(+6)cancel(-6)=6-6#

#rArr8x=0rArrx=0#

Substitute this value into ( 3 ) and evaluate for y

#x=0toy=0+2=2#

#rArr"point of intersection "=(0,2)#
graph{(y-2x-2)(y+2/3x-2)=0 [-10, 10, -5, 5]}