Math  /  Algebra

QuestionPractice and Problem-Solving Exercises MATHEMATICAL PRACTICES
Practice Tell whether the given equation has the ordered pair as a solution. See Problem 1.
8. y=x+6;(0,6)y=x+6 ;(0,6)
9. y=1x;(2,1)y=1-x ;(2,1)
10. y=x+3;(4,1)y=-x+3 ;(4,1)
11. y=6x;(3,16)y=6 x ;(3,16)
12. x=y;(3.1,3.1)-x=y ;(-3.1,3.1)
13. y=4x;(2,8)y=-4 x ;(-2,8)
14. y=x+23;(1,13)y=x+\frac{2}{3} ;\left(1, \frac{1}{3}\right)
15. y=x34;(2,114)y=x-\frac{3}{4} ;\left(2,1 \frac{1}{4}\right)
16. x5=y;(10,2)\frac{x}{5}=y ;(-10,-2)

Use a table, an equation, and a graph to represent each relationship.
17. Ty is 3 years younger than Bea.
18. The number of checkers is 24 times the number of checkerboards. (s) See Problem 2.
19. The number of triangles is 13\frac{1}{3} the number of sides.
20. Gavin makes $8.50\$ 8.50 for each lawn he mows.

Use the table to draw a graph and answer the question. - See Problem 3.
21. The table shows the height in inches of stacks
22. The table shows the length in centimeters of of tires. Extend the pattern. What is the a scarf you are knitting. Suppose the pattern height of a stack of 7 tires?

Stacks of Tires \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Number \\ of Tires, xx \end{tabular} & \begin{tabular}{c} Height of \\ Stack, yy \end{tabular} \\ \hline 1 & 8 \\ \hline 2 & 16 \\ \hline 3 & 24 \\ \hline 4 & 32 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Number \\ of Days, xx \end{tabular} & \begin{tabular}{c} Length of \\ Scarf, yy \end{tabular} \\ \hline 1 & 12.5 \\ \hline 2 & 14.5 \\ \hline 3 & 16.5 \\ \hline 4 & 18.5 \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? Given the equation x5=y\frac{x}{5} = y and the ordered pair (10,2)(-10, -2), we want to find out if the ordered pair is a solution to the equation. Watch out! Remember an ordered pair is written as (x,y)(x, y), so make sure you plug in the right values for xx and yy!

STEP 2

1. Substitute the values
2. Simplify and check

STEP 3

From the ordered pair (10,2)(-10, -2), we can see that x=10x = \mathbf{-10} and y=2y = \mathbf{-2}.

STEP 4

Let's **substitute** these values into our equation x5=y\frac{x}{5} = y.
This gives us 105=2\frac{\mathbf{-10}}{5} = \mathbf{-2}.

STEP 5

We simplify the left side of the equation: 105\frac{\mathbf{-10}}{5}.
Dividing 10-10 by 55 gives us 2\mathbf{-2}.

STEP 6

Now, our equation looks like this: 2=2\mathbf{-2} = \mathbf{-2}.
Since both sides of the equation are equal, the ordered pair (10,2)(-10, -2) *is* a solution!

STEP 7

Yes, the ordered pair (10,2)(-10, -2) is a solution to the equation x5=y\frac{x}{5} = y.

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