SOLUTION: addition method -x+6y=-2 5x-30y=10

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Question 684372: addition method
-x+6y=-2
5x-30y=10
Found 2 solutions by MathLover1, ReadingBoosters:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition


Lets start with the given system of linear equations

-1%2Ax%2B6%2Ay=-2
5%2Ax-30%2Ay=10

In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get -1 and 5 to some equal number, we could try to get them to the LCM.

Since the LCM of -1 and 5 is -5, we need to multiply both sides of the top equation by 5 and multiply both sides of the bottom equation by 1 like this:

5%2A%28-1%2Ax%2B6%2Ay%29=%28-2%29%2A5 Multiply the top equation (both sides) by 5
1%2A%285%2Ax-30%2Ay%29=%2810%29%2A1 Multiply the bottom equation (both sides) by 1


So after multiplying we get this:
-5%2Ax%2B30%2Ay=-10
5%2Ax-30%2Ay=10

Notice how -5 and 5 add to zero, 30 and -30 add to zero, -10 and 10 and to zero (ie -5%2B5=0) 30%2B-30=0, and -10%2B10=0)


So we're left with

0=0


which means any x or y value will satisfy the system of equations. So there are an infinite number of solutions


So this system is dependent

Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply the first equation by 5, then add the second equation
5(-x+6y=-2) to get -5x%2B30y=-10
...
-5x+30y = -10
5x - 30y = 10
-5x + 5x + 30y - 30y = -10 + 10
0 = 0
This a true statement; therefore, the system is dependent and every point on the line is a solution.
This is because they are the same line as seen when putting them both into slope intercept format.
...
-x + 6y = -2
6y = x-2
y = %281%2F6%29x+-+2%2F6
y = %281%2F6%29x+-+1%2F3
AND
5x - 30y = 10
-30y = -5x + 10
y = %285%2F30%29x+%2B+%2810%2F-30%29
y = %281%2F6%29x+-+%281%2F3%29
.....................
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