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

1 Answer
Feb 14, 2017

Answer:

#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#