Which of the following points is a solution to the system of equations y=23x−5

and y=73x−1
?(1 point)
Responses

(−1.2,3.3)
left parenthesis negative 1.2 comma 3.3 right parenthesis

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

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

(2.4,−6.6)

1 answer

To determine which of the given points is a solution to the system of equations \(y = 23x - 5\) and \(y = 73x - 1\), we can substitute the \(x\) values from each point into both equations and check if the corresponding \(y\) values match.

Let's test each point:

  1. Point (-1.2, 3.3):

    • For \(y = 23x - 5\): \[ y = 23(-1.2) - 5 = -27.6 - 5 = -32.6 \quad \text{(not equal to 3.3)} \]
    • For \(y = 73x - 1\): \[ y = 73(-1.2) - 1 = -87.6 - 1 = -88.6 \quad \text{(not equal to 3.3)} \]
  2. Point (-2.4, -6.6):

    • For \(y = 23x - 5\): \[ y = 23(-2.4) - 5 = -55.2 - 5 = -60.2 \quad \text{(not equal to -6.6)} \]
    • For \(y = 73x - 1\): \[ y = 73(-2.4) - 1 = -175.2 - 1 = -176.2 \quad \text{(not equal to -6.6)} \]
  3. Point (-2.4, 6.6):

    • For \(y = 23x - 5\): \[ y = 23(-2.4) - 5 = -55.2 - 5 = -60.2 \quad \text{(not equal to 6.6)} \]
    • For \(y = 73x - 1\): \[ y = 73(-2.4) - 1 = -175.2 - 1 = -176.2 \quad \text{(not equal to 6.6)} \]
  4. Point (2.4, -6.6):

    • For \(y = 23x - 5\): \[ y = 23(2.4) - 5 = 55.2 - 5 = 50.2 \quad \text{(not equal to -6.6)} \]
    • For \(y = 73x - 1\): \[ y = 73(2.4) - 1 = 175.2 - 1 = 174.2 \quad \text{(not equal to -6.6)} \]

None of the points provided satisfy both equations. Therefore, it looks like all options need to be reevaluated or checked for correct choices since no solution was found in the provided options. If there is a need to provide a different answer verifying possible points, please double-check those points.