Question

How do you solve the simultaneous equations `3x+7y=26` and `4x+5y=13`?

Answer 1

I found:
`x=-3`
`y=5`

Explanation:

I would multiply the first equation by `-4` and the second by `3` and add together the two equatins (in columns):
`{-12x-28y=-104`
`{12x+15y=39`
`0-13y=-65`
So: `y=65/13=5`
Substitute back this value into the first equation:
`3x+7*5=26`
`3x=26-35=-9`
`x=-9/3=-3`

Answer 2

`color(red)(x = -3, y = 5)` or `color(red)("(-3, 5)")`

Explanation:

One way is to use the method of elimination.

Step 1. Enter the equations.

Equation (1) `3x+7y = 26`
Equation (2) `4x+5y = 13`

Step 2. Prepare the equations.

Multiply every term in each equation by a number so that equal terms can be eliminated.

Multiply Equation (1) by `4` and Equation (2) by `3`.

Equation (3) `12x +28y = 104`
Equation (4) `12x +15y = 39`

Step 3. Subtract Equation (4) from Equation (3).

(3) `12x +28y = 104`
(4) `12x +15y = 39`
(5) `bar(color(white)(000000)13y = 65)`

`y = 65/13`

Equation (6) `y = 5`

Step 4. Substitute Equation (6) in Equation (2).

`4x+5y = 13`
`4x+5×5 =13`
`4x+25 = 13`
`4x = 13-25`
`4x=-12`
`x = -12/4`

`x = -3`

Solution: `x = -3, y = 5` or `(-3, 5)`

Check: Substitute the values of `x` and `y` in Equation (1).

`3x+7y = 3(-3) + 7×5 = -9+35= 26`