Question

How do you solve the system `4x-2y=16, 4x+2y=24` using graphing?

Answer 1

`x=5 and y=2`

Explanation:

Let us solve the linear system by :
`" "`
Multiplying one of the equations by an integer to eliminate one of the unknowns.
`" "`
Add the two equations.
`" "`
Solve for one unknown.
`" "`
Substitute the solution to find the second unknown.
`" "`
Solving the given linear system:
`" "`
`4x-2y=16` `" " Eq1`
`" "`
`4x+2y=24` `" "Eq2`
`" "`
In the given linear system the coefficients of `" "y" "`in both equations are given opposites.

Let's add both equations:
`" "`
`Eq1 + Eq2`
`" "`
`rArr4xcancel(-2y)+4xcancel(+2y)=16+24`
`" "`
`rArr8x=40`
`" "`
`" "`
`"rArrx=40/8`
`" "`
`rArrcolor(red)(x=5)`
`" "`
Substitute the value of `" "color(red)(x=5)" "` in `" "Eq1" "` to find `" "y`
`" "`
`4x-2y=16` `" " Eq1`
`" "`
`rArr4(color(red)5)-2y=16`
`" "`
`rArr20-2y=16`
`" "`
`rArr-2y=16-20`
`" "`
`rArr-2y=-4`
`" "`
`rArry=(-4)/(-2)`
`" "`
`rArrcolor(red)(y=2)`
`" "`
Therefore, `x=5 and y=2`