Question

Select the correct answer. What is the solution set of 4x = y and 2x2 − y = 0? A. {(0.5, -0.5), (2, -8)} B. {(0, 0), (2, 8)} C. {(1.5, 2), (8, 2)} D. {(-1.5, -2), (2, 8)}

Answer 1

We have to determine the solution set for the given equations:

$4x=y$ and $2x^2-y=0$

A. Let us consider the first solution set (0.5,-0.5)

Consider equation 4x = y

$(4 \times 0.5) = -0.5$

2 is not equal to -0.5

Hence, it is not the solution set for this equation.

Let us check for another set.

B. Consider the second solution set (0,0) and (2,8)

Consider equation 4x =y and solution set(0,0)

$(4 \times 0) = 0$

0 = 0

Hence, (0,0) is the solution set to this equation.

Consider equation 4x = y and set (2,8)

$(4 \times 2) = 8$

8 = 8

Hence, (2,8) is the solution to this equation.

Now, consider equation $2x^2-y =0$ and set (0,0)

$2(0)^2-0 =0$

0=0

So, this is the solution set to this equation.

Now, consider equation $2x^2-y =0$ and set (2,8)

$2(2)^2-8 =0$

8-8=0

So, 0=0

So, this is the solution set to this equation.

Therefore, Option B is the correct answer.

Answer 2

Answer:

B. {(0, 0), (2, 8)}

Step-by-step explanation:

This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations. It may be solved by substitution in that one of the variable is made the subject of the equation and the result is substituted into the second equation .

4x = y and 2x2 − y = 0

substituting y into equation 2

2x2 − 4x = 0

2x ( x - 2) = 0

2x = 0

or x - 2 = 0

when x = 0, y = 0

when x = 2, y = 8