Question

What is the solution to the system of equations?

Answer 1

Solve systems of equations by graphing. A system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system.

Answer 2

(7, 13/3)

Explanation:

`y=(1)/(3) x+2\\` Line up the equations on top of each other

`y=(4)/(3) x-5`

`-4*[y=(1)/(3) x+2]` Multiply the top equation by
`-4` in order to cancel out the
`x` variable

`-4y=-(4)/(3) x-8` Switch out the first equation for this one

`-4y=-(4)/(3) x-8` Line up the equations

`y=(4)/(3) x-5`

`-3y=-13` Add the two equations top to bottom, left to right

`y=(13)/(3)`

Now that you've found
`y`, you need to find
`x`. Just plug in the y-value to either of the equations in Step 1:

The first equation has smaller numbers, so let's use that one.

`(13)/(3) =(1)/(3) x+2`

To make it easier you can multiply all the terms in the equation by 3:

`13=x+6`

`7=x`

The
`x`- and
`y`- values together give a solution of (
`7`,
`(13)/(3)` )