The math teacher asked his students to determine a solution for 1.5x−2y=8. Which solution below is the correct one?(1 point)

Question

Responses

Fiona believes (4,7) is a solution.
Fiona believes left parenthesis 4 comma 7 right parenthesis is a solution.

Sam believes (−4,−7) is a solution.
Sam believes left parenthesis negative 4 comma negative 7 right parenthesis is a solution.

Mary believes (4,−7) is a solution.
Mary believes left parenthesis 4 comma negative 7 right parenthesis is a solution.

Peter believes (−4,7) is a solution.

Answer 1

To determine which pair is a solution for the equation $1.5x-2y=8$, we can substitute each pair of values into the equation and see if the equation holds true.

1. Fiona's solution (4, 7): $$1.5(4)-2(7)=6-14=-8(\text{Not a solution})$$

2. Sam's solution (-4, -7): $$1.5(-4)-2(-7)=-6+14=8(\text{This is a solution})$$

3. Mary's solution (4, -7): $$1.5(4)-2(-7)=6+14=20(\text{Not a solution})$$

4. Peter's solution (-4, 7): $$1.5(-4)-2(7)=-6-14=-20(\text{Not a solution})$$

The only solution that satisfies the equation $1.5x-2y=8$ is Sam's belief that $(-4,-7)$ is a solution.

Answer 2

Select the option below that correctly shows which of the following ordered pairs is part of the solution set for the equation y=4x+2.(1 point)
Responses

(3,45)
left parenthesis 3 comma 45 right parenthesis

(3,12)
left parenthesis 3 comma 12 right parenthesis

(3,7)
left parenthesis 3 comma 7 right parenthesis

(3,14)
left parenthesis 3 comma 14 right parenthesis

Answer 3

To determine which ordered pair is part of the solution set for the equation $y=4x+2$, we will substitute $x=3$ into the equation and find the corresponding value of $y$.

Substituting $x=3$: $$y=4(3)+2=12+2=14$$

So, when $x=3$, $y=14$. Therefore, the ordered pair $(3,14)$ is a solution of the equation.

Now, let’s check each option:

1. $(3,45)$: $$\text{Not a solution, since }y\ne 14.$$

2. $(3,12)$: $$\text{Not a solution, since }y\ne 14.$$

3. $(3,7)$: $$\text{Not a solution, since }y\ne 14.$$

4. $(3,14)$: $$\text{This is a solution, since }y=14.$$

The correct option is $(3,14)$.

Answer 4

Use the image to answer the question.

Which of the following ordered pairs is part of the solution set for the equation y=2x+5?

(1 point)
Responses

(7,1)
left parenthesis 7 comma 1 right parenthesis

(3,−1)
left parenthesis 3 comma negative 1 right parenthesis

(1,2)
left parenthesis 1 comma 2 right parenthesis

(1,7)
left parenthesis 1 comma 7 right parenthesis

Answer 5

To determine which ordered pair is part of the solution set for the equation $y=2x+5$, we will substitute the $x$ values from each ordered pair into the equation and see if the corresponding $y$ values match.

1. For (7, 1): $$y=2(7)+5=14+5=19(\text{not a solution})$$

2. For (3, −1): $$y=2(3)+5=6+5=11(\text{not a solution})$$

3. For (1, 2): $$y=2(1)+5=2+5=7(\text{not a solution})$$

4. For (1, 7): $$y=2(1)+5=2+5=7(\text{this is a solution})$$

The ordered pair that is part of the solution set for the equation $y=2x+5$ is $(1,7)$.

Answer 6

Use the image to answer the question.

Which of the following ordered pairs is part of the solution set for the equation y=5x2−2?

(1 point)
Responses

(1,5)
left parenthesis 1 comma 5 right parenthesis

(−1,43)
left parenthesis negative 1 comma 43 right parenthesis

(−1,5)
left parenthesis negative 1 comma 5 right parenthesis

(−1,3)
left parenthesis negative 1 comma 3 right parenthesis

Answer 7

To determine which ordered pair is part of the solution set for the equation $y=5x^2-2$, we will evaluate each pair by substituting the $x$ values into the equation and checking if the resulting $y$ values match.

1. For (1, 5): $$y=5(1^2)-2=5(1)-2=5-2=3(\text{not a solution since }y\ne 5)$$

2. For (−1, 43): $$y=5((-1{)}^2)-2=5(1)-2=5-2=3(\text{not a solution since }y\ne 43)$$

3. For (−1, 5): $$y=5((-1{)}^2)-2=5(1)-2=5-2=3(\text{not a solution since }y\ne 5)$$

4. For (−1, 3): $$y=5((-1{)}^2)-2=5(1)-2=5-2=3(\text{this is a solution since }y=3)$$

The ordered pair that is part of the solution set for the equation $y=5x^2-2$ is $(-1,3)$.