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

and y=73x−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)

1 answer

To determine which of the given points is a solution to the system of equations, we need to substitute the x-coordinate of each point into the equations \( y = 23x - 5 \) and \( y = 73x - 1 \) and see if we get the same y-coordinate from both equations.

Let's test each point:

1. Point \((-2.4, -6.6)\)

  • For \( y = 23x - 5 \): \[ y = 23(-2.4) - 5 = -55.2 - 5 = -60.2 \]
  • For \( y = 73x - 1 \): \[ y = 73(-2.4) - 1 = -175.2 - 1 = -176.2 \]
  • These do not match \( -6.6 \).

2. Point \((2.4, -6.6)\)

  • For \( y = 23x - 5 \): \[ y = 23(2.4) - 5 = 55.2 - 5 = 50.2 \]
  • For \( y = 73x - 1 \): \[ y = 73(2.4) - 1 = 175.2 - 1 = 174.2 \]
  • These do not match \( -6.6 \).

3. Point \((-2.4, 6.6)\)

  • For \( y = 23x - 5 \): \[ y = 23(-2.4) - 5 = -55.2 - 5 = -60.2 \]
  • For \( y = 73x - 1 \): \[ y = 73(-2.4) - 1 = -175.2 - 1 = -176.2 \]
  • These do not match \( 6.6 \).

4. Point \((-1.2, 3.3)\)

  • For \( y = 23x - 5 \): \[ y = 23(-1.2) - 5 = -27.6 - 5 = -32.6 \]
  • For \( y = 73x - 1 \): \[ y = 73(-1.2) - 1 = -87.6 - 1 = -88.6 \]
  • These do not match \( 3.3 \).

Since I've calculated all points, and none satisfy both equations, it appears there was a misunderstanding; however, the proper way to find a solution would be to set \( 23x - 5 = 73x - 1 \) and solve for \( x \):

  1. Set the equations equal: \[ 23x - 5 = 73x - 1 \]

  2. Rearranging gives: \[ -5 + 1 = 73x - 23x \] \[ -4 = 50x \implies x = -\frac{4}{50} = -\frac{2}{25} \]

  3. Substitute back to find \( y \): \[ y = 23(-\frac{2}{25}) - 5 = -\frac{46}{25} - \frac{125}{25} = -\frac{171}{25} \]

  4. You could continue looking for better approximation.

None of the listed points solve both equations. In practical exercises, check for appropriateness of your point listings or calculation methods.