How do you solve the system of equations -3x + 2y = - 15 and 2x = 4y + 26?

2 Answers
Apr 17, 2017

x=1; y=-6

Explanation:

equation (1) is -3x+2y=-15 and
equation (2) is 2x=4y+26.

From equation (2), we can divide by 2 and write:

equation (3) as 2y = x-13

Substitute into equation (1) to give:

-3x+(x-13) = -15; which means x=1.

Now, sub x=1 into equation (3),

2y = 1-13,
2y =-12

y = -6

Apr 17, 2017

x=1 and y =-6

Explanation:

color(white)(.....)-3x+2y =-15" "A
color(white)(.....)+2x-4y =+26" "B

Try to create additive inverses with the variables.

A xx 2: rarr color(white)(...)-6xcolor(blue)(+4y) =-30" "C
color(white)(........... ............)2xcolor(blue)(-4y) =+26" "B

C+B:color(white)(........)-4x " "= -4
color(white)(....................................)x =1

Substitute x=1 into B

color(white)(.....)+2x-4y =+26" "B
color(white)(.....)+2(1)-4y =+26
color(white)(..........)+2-4y =+26
color(white)(.................)-4y =+26-2
color(white)(.................)-4y =+24
color(white)(.........................)y =-6

Check in equation A:

-3(1) +2(-6) = -15
-3-12 = -15
color(white)(......)-15 = -15