Question

How do you solve the system of equations `3x+y=-2` and `-x+4y=18`?

Answer 1

The common point on the graph is `(x,y)->(-2,4)`

Calculation method shown in detail. With practice you will start to jump steps.

Explanation:

There are various ways of solving these. With these two perhaps the quickest is to use substitution. One has `x` on its own and the other has `y` on its own.

Given:`" "3x+y=-2` ...........................(1)
`" "-x+4y=18` ............................(2)

For equation (1) subtract `color(blue)(3x)` from both sides

`color(brown)(3xcolor(blue)(-3x)+y=-2color(blue)(-3x))`

But `3x-3x=0` giving

`0+y=-3x-2`

`y=-3x-2` ...............................(3)
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Substitute for `y` using equation (3) into equation (2)

`-x+4(-3x-2)=18`

Multiply everything inside the brackets by 4

`-x-12x-8=18`

`-13x-8=18`

Add `color(blue)(8)` to both sides

`color(brown)(-13x-8color(blue)(+8)=18color(blue)(+8))`

`-13x+0=26`

Divide both sides by `color(blue)(-13)`

`color(brown)((-13)/(color(blue)(-13)) x+0=26/(color(blue)(-13)))`

But `(-13)/(-13)=+1`

`color(green)(underline(bar(|" "x=-26/13 =-2" "|)))`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute `x=-26/13` into equation (1)

`color(brown)(3x+y=-2)color(blue)(" "->" "3(-26/13)+y=-2)`

`color(green)(underline(bar(|" "y=78/13-2 = 4" "|`
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