Question

Solve pair of simultaneous equations to find x and y

Answer 1

see explanation

Explanation:

Given the 2 equations

y = 6x → (1)

10x + 6y = 28 → (2)

Substitute y = 6x into (2)

10x + 6(6x) = 28

10x + 36x = 28

46x = 28 ( divide both sides by 46 )

x =
`(28)/(46)` =
`(14)/(23)`

Substitute this value into (1) for corresponding value of y

y = 6 ×
`(14)/(23)` =
`(84)/(23)`

Solution is (
`(14)/(23)`,
`(84)/(23)`)

Answer 2

x = 14/23

y=84/23

Explanation:

Easiest way is probably the way I' going to explain, but you could also use matrices if you want. Ask me if you'd like an explanation.

So there are several ways to handle this, personally I like to get one equation to a point where we have one variable equals everything else, we already have this with y=6x, so we can skip this step.

Now wherever there is y in the OTHER equation (that's important, don't do the same equation), plug in 6x instead. Then just solve for the variable. Good to note this gets a bit more complicated but stays pretty much the same with more than two variables. As long as you have enough equations.

10x + 6y = 28

10x + 6(6x) = 28

10x + 36x = 28

46x = 28

x = 28/46 = 14/23

Now we know what x equals, so you can plug that into either equation to solve for y. I think the first equation is a bit easier.

y = 6x

y = 6(14/23)

y = 84/23

You can plug these in to both equations to check and make sure they work as well.