Solve the system by the method of elimination

Question

2x-4y=6

-4x+8y=-12

If there is no solution, enter NO SOLUTION. If the system is dependent, enter a for x and enter y in terms of a.

Answer 1

Good evening,

When we use the elimination method for solving system of equations, we are trying to determine which solutions will make each equation true. The first step is to look at both your "x" values and your "y" values and ask yourself "Is there a number I can multiply (x or y value) by to make it equal to zero when I add each equation together?". Immediately when I look at this equation, I notice that if I multiply my "2x" by 2 then it will eliminate my "x" values. What I do to one term, I have to do to the entire equation. My new equation would be:

4x-8y=12

-4x+8y=-12

My next step is to add my equations, my answer comes out to 0=0. In this case, the system of equations is what we call "dependent". They are different ways of expressing the same equation of the same line. The directions tell us "if the system is dependent, enter a for x and enter y in terms of a". How we do that is find each "x" and substitute the letter "a" into the equation instead of x. We will have:

2a-4y=6

Next, we solve for "y". My first step will be to subtract 2a from each side:

2a-4y= 6

-2a = 6-2a

The resulting equation is:

-4y= 6- 2a

Next I'm going to divide each side by -4 so I can isolate my "y".

-4y= 6-2a

-4 -4

My resulting equation is y= 6-2a.

4

Some teachers will accept your "y" value in this form. So your ordered pair would be (a, 6-2a)

4 .

Some teachers may require you to factor it out further see the following steps. You'll notice that the "a" term is negative so I need to factor out a -2. Since everyone on the right side of the equation is divisible by -2, this will work. The resulting equation should be:

y= -2(-3+a)

-2(-2)

Lastly, I'm going to rearrange my equation so that my "a" term is in the front. The equation now reads:

y= -2(a-3)

-2(-2)

Finally, our ordered pair should be the following:

(a, -2(a-3) )

-2(-2)

I hope this helps!

Carly

I'm also going to rearrange my equation so the "a" is in the front. These 2 changes result in the following equation:

y= 2(-