Question

How do you write the the ordered pair that is the solution to the following system of equations: 5x - 2y = 3 and 3x + 4y = 7?

Answer 1

`(1, 1)`

Explanation:

The ordered pair is the set of values of `x` and `y` which can satisfy a given set of algebraic equations and written as `(x, y)` for 2D and as `(x, y, z)` for 3D.

For the set of equations;

`5x - 2y = 3`

`3x + 4y = 7`

We can get the ordered pair by solving them as follows:

Rearranging the 1st equation we have,

`(5x - 3 )/2 = y`

Then, we can substitute this `y` into the 2nd equation,

`=> 3x + 4 *(5x - 3 )/2 = 7`

`=> 3x + 10x - 6 = 7`

`=> 13x = 13`

`=> x = 1`

put the value of `x` back in the 1st equation to get `y`,

`y = (5*1 - 3 )/2`

`=> y = 1`

Therefore, the solution is written in the ordered pair form as

`(x, y ) = (1, 1)`

Answer 2

The solution is `x =1 and y=1`

As an ordered pair it is `(1,1)`

Explanation:

To solve the system of equations you can use several methods.
In this case I would choose elimination of the `y` terms.

`color(white)(..............)5x-2y = 3" "A`
`color(white)(..............)3x+4y=7" "B`

`A xx 2: " "10x-4y =6" "C`
`B+C:" "13x" " = 13`

`color(white)(..................)x=1`

Now that you know the value for `x`, substitute to find a value for `y`

`3(1) +4y =7`
`3+4y=7`
`4y=4`
`y=1`

The solution is `x =1 and y=1`
As an ordered pair it is `(1,1)`