Question

How do you solve the following linear system: `2x-5y=-4, x + 6y = 4,`?

Answer 1

`x=-4/17`

`y=color(white)("dd")12/17`

Explanation:

This is one of two approaches:

Given:
`2x-5y=-4" "..........Equation(1)`
`color(white)("d") x+6y=+4" "..........Equation(2)`

Multiply both sides of `Eqn(2)` by 2

`2x-color(white)("d")5y=-4" ".........Equation(1)`
`ul(2x+12y=+8" ".........Equation(2_a)larr" Subtract" )`
`color(white)("d")0-17y=-12`

By choosing negative it will change the `y` term into positive.
Divide both sides by `(-17)`

`color(blue)(color(white)("ddddddddddd")ul(bar(| color(white)(..) y=12/17color(white)(..)|)))`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Substitute for `color(red)(y=12/17)` into `Eqn(2)`

`color(green)(x+6color(red)(y)=4 color(white)("dddd")->color(white)("dddd")x+(6color(red)(xx12/17))=4 )`

`color(white)("ddddddddddddd")->color(white)("dddd")x+color(white)("ddd")72/17color(white)("d.d")=4`

`color(blue)(color(white)("ddddddddddd")ul(bar(| color(white)(..) x=-4/17color(white)(..)|)))`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Check")`

`2x-5y=-4" "..........Equation(1)`
`color(white)("d")x+6y=+4" "..........Equation(2)`

`2(-4/17)-5(12/17)=-4" "..........Equation(1)`
`color(white)("d")(-4/17)+6(12/17)=+4" "..........Equation(2)`

`-8/17-60/17=-4" "..........Equation(1)`
`-4/17+72/17=+4" "..........Equation(2)`

`-4=-4" "..........Equation(1)`
`+4=+4" "..........Equation(2)`