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

1 Answer
Feb 14, 2017

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