Question

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

Answer 1

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)`

Answer 2

`"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`