Question

How do you solve 4x - 3y = 33 and x = - 4y - 25?

Answer 1

Point of intersection (lines cross) `->(x,y)=(3,-7)`

Explanation:

Given:

`4x-3y=33`.................................(1)
`x=-4y-25`.................................(2)

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`color(blue)("Determine the common value of y")`

Using equation (2) substitute for `x` in equation (1)

`4(-4y-25)-3y=33color(white)(.).........................(1_a)`

`-16y-100-3y=33`

`-19y-100=33`

Multiply both sides by (-1)

`+19y+100=-33`

Subtract 100 from both sides

`19y+0=-133`

Divide both sides by 19

`color(blue)(y=-133/19 = -7)`
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`color(blue)("Determine the common value of "x)`

Substitute the value of `y` into equation (2)

`color(brown)(x=-4y-25)" "color(green)( ->" " x=-4(-7)-25)`

`color(blue)(x=+3)`
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