ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos

Solving Systems of Equations by Graphing 16936 Views


Share It!


Description:

To solve systems of equations by graphing, just simplify the equations to be in slope intercept form (y = mx + b), and then graph them. Finally, find the intersection point... and you have your variable values. Easy... right?

Language:
English Language

Transcript

00:04

Solving Systems by Graphing a la Shmoop. The mayor of New Chunk City has banned all

00:13

sugary beverages larger than sixty-four ounces.

00:19

You've heard from a friend that Black's Market is selling sixty-four ounce sodas in the alleyway

00:24

behind the store.

00:27

Unfortunately, you don't know where Black's Market is, and all you have are a couple of

00:33

cryptic equations leading the way there.

00:36

Graph the equations, and they'll provide you with the coordinates to sugar overload.

00:40

Here's the scrap of paper your friend gave you.

00:45

We'll tackle the equations by changing them to slope-intercept form first...

00:50

Let's start with the top equation...

00:52

negative-three-x plus y equals six. You can do this one without sugar and caffeine

00:57

coursing through your veins.

00:59

Just add three-x to both sides. Doing that, we see that y equals three-x plus six.

01:05

The second one is slightly trickier. But if you can mix Coke and Pepsi until it tastes

01:09

like Dr. Pepper, this is nothing.

01:11

First, subtract x from both sides, giving us two-y equals negative x minus 2.

01:19

Then just divide all the terms by two.

01:21

We end up with y equals negative one-half x minus 1.

01:26

Now we just have to graph them.

01:29

We'll do the first equation in blue.

01:33

The y-intercept is 6, so we can plot a point at zero-six, which is six up the y-axis.

01:40

Because we know slope is rise over run, for every one we run or move to the right along

01:45

the x axis, we rise, or move three up the y-axis.

01:49

Reversing this, we move three spaces down the y-axis for every one we move left along

01:55

the x-axis.

01:57

The blue line will intersect the x-axis at negative-two, zero.

02:02

We'll do the second equation in red.

02:04

The y-intercept is negative 1, so we can plot a point at zero, negative-one on the y-axis.

02:11

For every one we run, or move right along the x-axis, we'll move one-half down.

02:17

Flipping that, we'll move 1/2 up for every one we move left along the x-axis.

02:21

This line, too, intersects the x-axis at negative-two, zero.

02:29

So that's where the Black's Market is.

02:32

At (-2, 0).

02:34

You may have to take the subway there, but we're pretty sure you'll be able to run back

02:37

home on a pure sugar rush.

Up Next

Solving Systems of Linear Inequalities
11428 Views

How do you solve a system of linear inequalities? Aw, man...and we thought solving a problem like Maria was tough...

Related Videos

Solving Systems of Linear Equations in Three Variables
823 Views

Please note: If starting your own petting zoo, Shmoop recommends you stock it with animals that aren’t quite so likely to bite your hand off. Tha...

Solving Systems of Equations by Substitution
14325 Views

We just love us some alliteration.

Solving Systems of Equations by Elimination
8201 Views

Solving systems of equations by elimination: Survivor-style. Sorry, y... the tribe as spoken.

ACT Math 3.4 Intermediate Algebra
641 Views

ACT Math: Intermediate Algebra Drill 3, Problem 4. Solve this system.