How do you solve the following linear system: -3x + 2y = 1 , x + 1/2y = 7 ?

2 Answers
Apr 1, 2017

Find the x value using one off the equations.

x+1/2y=7
x=7-1/2y

Plug the x value into the other equation.

-3(7-1/2y)+2y=1

Simplify

-21+3/2y+2y=1

3/2y+2y=22

3/2y+4/2y=22

7/2y=22

y=(22(2))/7

y=44/7

Plug in the y value to find the x value.

x+1/2(44/7)=7

x+22/7=7

x=49/7-22/7

x=27/7

ANSWER: (27/7,44/7)

Apr 1, 2017

"answer:" x=27/7" , "y=44/7

Explanation:

-3x+2y=1" "(1)

x+1/2y=7" "(2)

"let us multiply both sides of equation (2) by 4"

color(red)(4)*(x+1/2y)=color(red)(4)*7

"We get ;"

4x+2y=28" "(3)

"the coefficients of term 'y' in both equation (1) and (3) is equal."

"let subtract (3) from (1) to eliminate 'y'"

-3x+2y-(4x+2y)=1-28

-3x+2y-4x-2y=-27

-3x+cancel(2y)-4x-cancel(2y)=-27

-7x=-27

x=27/7

"now ,let us use (1) or (2)"

x+1/2y=7

27/7+y/2=7

y/2=7-27/7

y/2=(49-27)/7

y/2=22/7

y=44/7