Question

Solve the system of equations and choose the correct ordered pair.2x + 6y = 63x – 2y = 20

Answer 1

The first step I would do is split this into two functions so we can work with this system hand to hand. This is what it will look like:

$2x + 6y = 20$

$63x - 2y = 20$

It's easier to employ math strategies for system of equations when it is written like this.

Now, we are going to multiply every term in the second equation by 3. The reason for this is because we want to cancel either the x's or the y's, and if we multiply the bottom equation by 3, then the y becomes -6y, which we can combine with the +6y in the first equation to cancel out the y's. The first step looks like this:

$2x + 6y = 20$

$189x - 6y = 60$

(every number in the second equation was multiplied by 3)

Now, we can combine both of these equations into one, by combining each term seperately. In other words, the 189x and the 2x combine into 191x, the 6y and -6y cancel each other out, and the 60 and 20 on the right side of the equal sign combine into 80. This is what it looks like after combining:

$191x = 80$

Now, we just solve for x:

$x = \frac{80}{191}$

Now that we have x, we can plug it in into one of the other equations to get y. It will be easier to plug x into the first equation, since 2 and 6 tend to be smaller numbers:

$2 (\frac{80}{191}) + 6y = 20$

Multiply the fraction by 2:

$\frac{160}{191} + 6y = 20$

Subract the fraction on both sides:

$6y = 20 - \frac{160}{191}$

Divide both sides by 6:

$y = \frac{20 - \frac{160}{191} }{6}$

Im going to use my calculator to simplify y. If you want to know how to simply this, let me know in the comments:

$y = \frac{610}{191}$

So finally, our ordered pair, and the answer itself is:

$( \frac{80}{191} \: \frac{610}{191} )$

(With a comma between both numbers)

Let me know if you have any questions or concerns in the comments ;)