Question

Two linear equations are represented by using the tables below.

A 2-column table with 4 rows titled Equation A. Column 1 is labeled x with entries negative 2, 0, 3, 4. Column 2 is labeled y with entries negative 8, negative 2, 7, 10.
A 2-column table with 4 rows titled Equation B. Column 1 is labeled x with entries negative 3, negative 1, 1, 5. Column 2 is labeled y with entries negative 9, negative 5, negative 1, 7.

The data points for equation A are graphed on the coordinate plane below and are connected by using a straight line.

On a coordinate plane, a line goes through (0, negative 2) and (2, 4).

What is the solution to the system of equations?
(–2, –8)
(–1, –5)
(0, –2)
(2, 4)

Answer 1

To find the solution to the system of equations represented by the given tables, we first need to determine the equations of both lines based on the provided points.

**For Equation A:**
The points given in Table A are:
- (-2, -8)
- (0, -2)
- (3, 7)
- (4, 10)

To find the equation of the line, we can use two points. Let's consider the points (0, -2) and (4, 10).

1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - (-2)}{4 - 0} = \frac{12}{4} = 3
\]

2. **Use the point-slope form (y - y_1 = m(x - x_1))** with point (0, -2):
\[
y - (-2) = 3(x - 0) \implies y + 2 = 3x \implies y = 3x - 2
\]

So, the equation for Equation A is:
\[
y = 3x - 2
\]

**For Equation B:**
The points given in Table B are:
- (-3, -9)
- (-1, -5)
- (1, -1)
- (5, 7)

Let's take points (-3, -9) and (5, 7).

1. **Calculate the slope (m)**:
\[
m = \frac{7 - (-9)}{5 - (-3)} = \frac{7 + 9}{5 + 3} = \frac{16}{8} = 2
\]

2. **Use the point-slope form with point (5, 7)**:
\[
y - 7 = 2(x - 5) \implies y - 7 = 2x - 10 \implies y = 2x - 3
\]

So, the equation for Equation B is:
\[
y = 2x - 3
\]

**To find the solution to the system of equations, we need to find the intersection of the two lines:**
1. Set the equations equal:
\[
3x - 2 = 2x - 3
\]

2. Solve for \(x\):
\[
3x - 2x = -3 + 2 \implies x = -1
\]

3. Substitute \(x = -1\) back into either equation to find \(y\):
\[
y = 3(-1) - 2 = -3 - 2 = -5
\]

Therefore, the solution to the system of equations is:
\[
(-1, -5)
\]

So, the correct answer is \((–1, –5)\).