Math  /  Algebra

QuestionSolve by Graphing: {y=14x8y=x5\left\{\begin{array}{l} y=\frac{1}{4} x-8 \\ y=x-5 \end{array}\right.

Studdy Solution

STEP 1

What is this asking? Find the (x,y)(x, y) values that make both equations true at the same time! Watch out! Make sure your lines are straight and accurate, a tiny mistake can lead to the wrong answer!

STEP 2

1. Set up the graph
2. Graph the first line
3. Graph the second line
4. Find the intersection

STEP 3

Alright, let's **draw** some axes!
Make sure your xx and yy axes are clearly labeled.
Give yourself plenty of space, because a larger graph makes it easier to see the solution!

STEP 4

Our first equation is y=14x8y = \frac{1}{4}x - 8.
The **y-intercept** is 8-8, so we **plot** the point (0,8)(0, -8).

STEP 5

The **slope** is 14\frac{1}{4}, which means for every **11 step** we take to the right along the xx-axis, we take 14\frac{1}{4} of a step up the yy-axis.
So from (0,8)(0, -8), we can **plot** another point at (0+1,8+14)(0 + 1, -8 + \frac{1}{4}), which simplifies to (1,734)(1, -7\frac{3}{4}).

STEP 6

Now, **draw** a straight line through those two points.
Extend the line across the whole graph.
Boom! First line done!

STEP 7

Our second equation is y=x5y = x - 5.
The **y-intercept** is 5-5, so we **plot** the point (0,5)(0, -5).

STEP 8

The **slope** is 11, or 11\frac{1}{1}.
This means for every **11 step** to the right, we take **11 step** up.
So from (0,5)(0, -5), we **plot** another point at (0+1,5+1)(0 + 1, -5 + 1), which simplifies to (1,4)(1, -4).

STEP 9

**Draw** a straight line through these two points and extend it across the graph.
Awesome! Second line done!

STEP 10

Look closely!
Where do the two lines cross?
That's our solution!
The xx and yy values at that point satisfy *both* equations.

STEP 11

The lines intersect at the point (4,1)(4, -1).
So, x=4x = 4 and y=1y = -1.

STEP 12

The solution to the system of equations is x=4x = 4 and y=1y = -1.
This means that when xx is 44 and yy is 1-1, both equations are true!

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord