Question

How do you solve the following system?: `-1/2x+5y=-20 , y=1-3x`

Answer 1

Answer given in extreme detail so that you can see what is happening. With practise you should be able to do this in 4 to 5 lines.

`color(blue)(color(white)(...)(x,y) -> (1 19/31 ,3 26/31)`

Explanation:

Given:
`-1/2x+5y=-20.....................................(1)`
`y=1-3x..................................................(2)`

`color(blue)("To find the value of x")`

Substitute for y in (1) using (2)

`-1/2x +5(1-3x)=-20...........................(1_a)`

Multiplying out the brackets
`-1/2 x-15x+5=-20`

Adding the x-terms
`-31/2 x+5=-20`

Collecting like terms
`-31/2x=-25`

Multiply both sides by 2
`-31x=-50`

Multiply both sides by (-1)
`31x=50`

Divide both sides by 31
`x=50/31..........................................(3)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find the value of y")`

Substitute equation (3) into equation (2) giving

`y=1-3x -> y=1-3(50/31)`

`y=1 - 150/31`

`y=-119/31 =-3 26/31`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together")`

The point of intersection of the two graphs/equations is:

`(x,y) -> (1 19/31 ,3 26/31)`