Question

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)

Answer 1

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.