Question

Solve the simultaneous equations 4x+8y=-4 2y-5x=23

Answer 1

y is equal to 1.5, and x is equal to -4

Explanation:

given:

`4x + 8y = -4`

`2y - 5x = 23`

We can start by factoring 4 out of the first equation:

`x + 2y = -1`

Now let's multiply it by -5:

`-5x - 10y = 5`

We'll rearrange the other equation to match that (just for clarity):

`-5x + 2y = 23`

Now let's subtract the modified equation from that:

`\begin{array}{c}-5x + 2y = 23\\-5x - 10y = 5\\ \ \ \ \ \ \ \ \ \ \ 12y = 18\end{array}`

So y is equal to 18/12, or 1.5

Let's plug that into one of the first equations and see what we get:

`2y - 5x = 23\\2(1.5) - 5x = 23\\3 - 5x = 23\\-5x = 20\\x = -4`

Giving us an x value of negative four. Let's plug that into the other equation to confirm:

`4x + 8y = -4\\4(-4) + 8y = -4\\-16 + 8y = -4\\-4 + 2y = -1\\2y = 3\\y = 1.5`

That matches up, so our answer is correct.

Answer 2

x = -4, y = 3/2

Explanation:

simplify the 1st equation by dividing each term by 4 to get:

x + 2y = -1

-5x + 2y = 23

Subtract to get: 6x = -24

x = -4

find 'y': 2y - 5(-4) = 23

2y + 20 = 23

2y = 3

y = 3/2