Which of the following points is a solution to the system of equations y=(2/3)x−5

Question

and y=(7/3)x−1
?(1 point)
Responses

(−2.4,−6.6)
left parenthesis negative 2.4 comma negative 6.6 right parenthesis

(2.4,−6.6)
left parenthesis 2.4 comma negative 6.6 right parenthesis

(−2.4,6.6)
left parenthesis negative 2.4 comma 6.6 right parenthesis

(−1.2,3.3)

Answer 1

To determine which of the given points is a solution to the system of equations

1. \( y = \frac{2}{3}x - 5 \)
2. \( y = \frac{7}{3}x - 1 \)

we will substitute each point into both equations and check if it satisfies both.

Check Point (−2.4,−6.6)

• For the first equation: \[ y = \frac{2}{3}(-2.4) - 5 = -1.6 - 5 = -6.6 \] This point satisfies the first equation.

• For the second equation: \[ y = \frac{7}{3}(-2.4) - 1 = -5.6 - 1 = -6.6 \] This point satisfies the second equation.

Since both equations are satisfied, (−2.4, −6.6) is a solution.

Check Point (2.4,−6.6)

• For the first equation: \[ y = \frac{2}{3}(2.4) - 5 = 1.6 - 5 = -3.4 \] This point does not satisfy the first equation.

Check Point (−2.4, 6.6)

• For the first equation: \[ y = \frac{2}{3}(-2.4) - 5 = -1.6 - 5 = -6.6 \] Does not equal 6.6.

Check Point (−1.2, 3.3)

• For the first equation: \[ y = \frac{2}{3}(-1.2) - 5 = -0.8 - 5 = -5.8 \] Does not equal 3.3.

After checking all points, the only point that satisfies both equations is:

(−2.4, −6.6).