Answer:
(3,0)
Explanation:
We will assume the question is the find a solution to the given series of equations. A "solution" will be any common point for which both lines intersect.
The solution can be found both graphically and mathematically. Both are used.
Graphical Solution
Both lines are plotted on a graph and the point(s) at which they intersect are solution(s). See the attached graph. There is only one intersection point, (3,0). This point satisfies both equations.
Mathematical Solution
8x+8y=24 and 4x-6y=12
Rearrange one of the equations to isolate x or y.
8x+8y=24
x+y = 3 [divide both sides by 8]
x = -y+3
Now use this definition of x in the second equation:
4x-6y=12
2x - 3y = 6 [divide both sides by 3]
2(-y+3) - 3y = 6 [substitute the x from above (x = -y+3)]
-2y + 6 -3y = 6
-5y = 0
y = 0 This is the value of y for a soultion.
Using y=0, find x:
x = -y+3
x = -(0)
x = +3 This is the x value of the solution
Solution: (3,0).