Question
The graph shows the system of equations below.
2 x minus 3 y = negative 6. y = negative one-third x minus 4
mc018-2.jpg
Which statement is supported by the graph?
The blue line represents the equation mc018-3.jpg, and the solution to the system of equations is (–6, –2).
The blue line represents the equation mc018-4.jpg, and the solution to the system of equations is ( –2, –6).
The red line represents the equation mc018-5.jpg, and the solution to the system of equations is (2, –4).
The red line represents the equation mc018-6.jpg, and the solution to the system of equations is (–4, 2).
2 x minus 3 y = negative 6. y = negative one-third x minus 4
mc018-2.jpg
Which statement is supported by the graph?
The blue line represents the equation mc018-3.jpg, and the solution to the system of equations is (–6, –2).
The blue line represents the equation mc018-4.jpg, and the solution to the system of equations is ( –2, –6).
The red line represents the equation mc018-5.jpg, and the solution to the system of equations is (2, –4).
The red line represents the equation mc018-6.jpg, and the solution to the system of equations is (–4, 2).
Answers
GPT-4o mini
To determine which statement is supported by the graph, we need to identify the equations represented by the blue and red lines and the point where they intersect.
1. **Equations in the System**:
- The first equation is \( 2x - 3y = -6 \). We can rewrite it in slope-intercept form (y = mx + b):
\[
2x + 6 = 3y \implies y = \frac{2}{3}x + 2
\]
- The second equation is \( y = -\frac{1}{3}x - 4 \).
2. **Identifying the Lines**:
- The **blue line** represents the equation \( y = -\frac{1}{3}x - 4 \).
- The **red line** represents the equation \( y = \frac{2}{3}x + 2 \).
3. **Finding the Intersection Point**:
To find the solution to the system of equations, we set the two equations equal to each other:
\[
-\frac{1}{3}x - 4 = \frac{2}{3}x + 2
\]
To eliminate the fractions, multiply through by 3:
\[
-x - 12 = 2x + 6
\]
Combine like terms:
\[
-x - 2x = 6 + 12 \implies -3x = 18 \implies x = -6
\]
Substitute \( x = -6 \) back into one of the equations to find \( y \):
\[
y = -\frac{1}{3}(-6) - 4 = 2 - 4 = -2
\]
Therefore, the solution to the system is at the point \( (-6, -2) \).
4. **Evaluating the Statement**:
Only the first statement matches what we found:
- The blue line represents the equation \( y = -\frac{1}{3}x - 4 \), and the solution to the system of equations is \( (-6, -2) \).
**Conclusion**: The correct statement that is supported by the graph is:
"The blue line represents the equation \( y = -\frac{1}{3}x - 4\), and the solution to the system of equations is \( (-6, -2) \)."
1. **Equations in the System**:
- The first equation is \( 2x - 3y = -6 \). We can rewrite it in slope-intercept form (y = mx + b):
\[
2x + 6 = 3y \implies y = \frac{2}{3}x + 2
\]
- The second equation is \( y = -\frac{1}{3}x - 4 \).
2. **Identifying the Lines**:
- The **blue line** represents the equation \( y = -\frac{1}{3}x - 4 \).
- The **red line** represents the equation \( y = \frac{2}{3}x + 2 \).
3. **Finding the Intersection Point**:
To find the solution to the system of equations, we set the two equations equal to each other:
\[
-\frac{1}{3}x - 4 = \frac{2}{3}x + 2
\]
To eliminate the fractions, multiply through by 3:
\[
-x - 12 = 2x + 6
\]
Combine like terms:
\[
-x - 2x = 6 + 12 \implies -3x = 18 \implies x = -6
\]
Substitute \( x = -6 \) back into one of the equations to find \( y \):
\[
y = -\frac{1}{3}(-6) - 4 = 2 - 4 = -2
\]
Therefore, the solution to the system is at the point \( (-6, -2) \).
4. **Evaluating the Statement**:
Only the first statement matches what we found:
- The blue line represents the equation \( y = -\frac{1}{3}x - 4 \), and the solution to the system of equations is \( (-6, -2) \).
**Conclusion**: The correct statement that is supported by the graph is:
"The blue line represents the equation \( y = -\frac{1}{3}x - 4\), and the solution to the system of equations is \( (-6, -2) \)."