How do you solve 2x+3y=62x+3y=6 and 2x-y=-22x−y=−2 using substitution?
1 Answer
Apr 5, 2017
Explanation:
To solve by
color(blue)"substitution"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−y=−2→(1)
2x+3y=6to(2)2x+3y=6→(2) Rearrange ( 1 ) to obtain y in terms of x , avoiding the use of fractions.
rArry=2x+2to(3)⇒y=2x+2→(3)
color(blue)"Substitute "Substitute into equation ( 2 )
2x+3(color(red)(2x+2))=6larrcolor(red)" and solve for x"2x+3(2x+2)=6← and solve for x
rArr2x+6x+6=6⇒2x+6x+6=6
rArr8x+6=6⇒8x+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]}
