Question

How do you solve the system of equations `x + 8y = 26` and `2x + y = 5`?

Answer 1

The solution is `(14/15, 47/15)`.

Explanation:

Equation 1: `x+8y=26`

Equation 2: `2x+y=5`

I am going to use elimination and substitution to answer this question.

Multiply Equation 1 by `-2`.

`-2(x+8y)=26xx-2`

`-2x-16y=-52`

Add the equations.

`-2x-16y=-52`
`color(white)(..)` `2x+color(white)(..)y=color(white)(......)5`
`-------`
`-15ycolor(white)(.........)=-47`

Divide both sides by `-15`.

`y=(-47)/(-15)`

`y=47/15`

Substitute `47/15` for `y` in Equation 1 and solve for `x`.

`x+8(47/15)=26`

`x+376/15=26`

Subtract `376/15` from both sides.

`x=-376/15+26`

Multiply `26` by `15/15`.

`x=-376/15+26xx15/15`

`x=-376/15+390/15`

`x=14/15`

Solution: `(14/15, 47/15)`

graph{(x+8y-26)(2x+y-5)=0 [-10, 10, -5, 5]}