ShmoopTube

00:03

Can you hear the people shmoop?

00:05

Which of the following graphs represents the solution to the following system of equations:

00:10

And here are the potential answers…

00:17

Okay, so to solve this problem, we basically need to figure out what the lines would look

00:21

like that are represented by this system of equations…

00:24

…and then use the eyeball test to match it up with its twin.

00:27

Okay, so first we need to find the point of intersection of the lines.

00:31

What x value and y value will work for both?

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If we multiply the first equation by -2… we’ll get -2x… meaning we can add it to

00:39

the bottom equation and be left with a single variable.

00:43

-2x – 2y = -4… plus 2x + 3y = 3…

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…gives us y = -1.

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Plugging that back into the first equation, we get an x value of 3.

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So our point where these two lines get up close and personal? (3, -1)

01:00

That’ll rule out C and D, which both have different points of intersection. So long, fellas.

01:05

So we’re down to A and B…

01:06

We can figure out which one to nix by putting both of the given formulas into slope-intercept form...

01:12

The first one becomes y = -x + 2 and the second becomes y = -2/3x + 1…which tells us that

01:21

we’re dealing with two negative slopes.

01:23

Only B fits the bill.

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As in, “Bicycle built for two.”

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