Question

How do you solve `4x + y = 26` and `5x - 2y =13`?

Answer 1

The solution is the point `(5,6)`.

Explanation:

Equation 1: `4x+y=26`

Equation 2: `5x-2y=13`

We can use addition/elimination and substitution to solve this system.

Multiply Equation 1 by `2`.

`2(4x+y)=26xx2`

Simplify.

`8x+2y=52`

Add Equation 1 and 2.

`8x+2y=52`
`5x-2y=13`
`-----`
`13x` `color(white)(.......)=65`

Divide both sides by `13`.

`x=65/13`

`x=5`

Substitute `5` for `x` in Equation 2 and solve for `y`.

`5(5)-2y=13`

`25-2y=13`

Subtract `25` from both sides.

`-2y=13-25`

`-2y=-12`

Divide both sides by `-2`.

`y=(-12)/(-2)` `larr` Two negatives make a positive.

`y=6`

The solution is the point `(5,6)`.

graph{(4x+y-26)(5x-2y-13)=0 [-9.33, 10.67, 0.08, 10.08]}