SOLUTION: Solve and CHECK the system of equations by either substitution or addition method. PLEASE! SHOW ALL WORK AND EVERY STEP. State what method you used and then show what x and Y=

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Question 969294: Solve and CHECK the system of equations by either substitution or addition method. PLEASE! SHOW ALL WORK AND EVERY STEP. State what method you used and then show what x and Y=
3x=-4y+15
8y=-6x+30
Found 2 solutions by Alan3354, Boreal:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
3x=-4y+15 --> 3x + 4y = 15
8y=-6x+30 --> 6x + 8y = 30
=================
3x + 4y = 15
6x + 8y = 30 Divide by 2 --> 3x + 4y = 15
-----------------
3x + 4y = 15
3x + 4y = 15
-------------------- Subtract (elimination)
0 = 0
It's the same equation twice --> dependent.
No unique solution.

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
Let's isolate the y variable, since 4 and 8 are factors. We could also do it with x, since 3 and 6 are factors.
the top equation becomes 3x-15=-4y
the bottom equation -6x+30=8y I moved the y to the right side and the x and constant to the left.

Notice that if we multiply the top equation by 2, we will have -8y on the right in the first and +8y on the right in the second.
These will add to zero.
2(3x-15=-4y) is 6x-30=-8y
Bottom -6x+30=8y
These add to zero 0+0=0
The two equations are identical. That means that either one may be used to show the relation between y and x.
Using the bottom equation, dividing both sides by 8
(-6/8)x +(30/8)=8y/8
(-3/4)x + (15/4)=y
This is a line with y-intercept (15/4), or 3.75 and slope -(3/4). Anything on that line will be a solution for x and y, such as x=0 y=3.75 or y=0 x=5.
Stated another way, there are an infinite number of solutions, which fall along the infinite number of points on a line.