Answer :
To solve the system of equations and find the solution graphically, follow these steps:
### Task 1: Graph the Equations
#### Equation 1: [tex]\( 2x - 3y = -18 \)[/tex]
1. Convert to Slope-Intercept Form (y = mx + b):
[tex]\[ 2x - 3y = -18 \][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[ -3y = -2x - 18 \][/tex]
[tex]\[ y = \frac{2}{3}x + 6 \][/tex]
2. Plot the Line:
- Start by plotting the y-intercept ([tex]\( b \)[/tex]): [tex]\((0, 6)\)[/tex]
- Use the slope [tex]\( \frac{2}{3} \)[/tex] (rise over run):
- From [tex]\((0, 6)\)[/tex], move up 2 units and right 3 units to find another point, which gives you [tex]\((3, 8)\)[/tex].
- Draw the line passing through these points.
#### Equation 2: [tex]\( 3x + y = -5 \)[/tex]
1. Convert to Slope-Intercept Form (y = mx + b):
[tex]\[ 3x + y = -5 \][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[ y = -3x - 5 \][/tex]
2. Plot the Line:
- Start by plotting the y-intercept ([tex]\( b \)[/tex]): [tex]\((0, -5)\)[/tex]
- Use the slope [tex]\( -3 \)[/tex] (rise over run):
- From [tex]\((0, -5)\)[/tex], move down 3 units and right 1 unit to find another point, which gives you [tex]\((1, -8)\)[/tex].
- Draw the line passing through these points.
### Task 2: Determine the Solution
The solution to the system of equations is the point where the two lines intersect.
- Intersection Point: Observe the graph to find the coordinates where the two lines cross.
Given the solution to the system is:
[tex]\[ x = -3, \quad y = 4 \][/tex]
### Task 3: Plot the Solution
Using the Mark Feature tool:
- Mark the point [tex]\((-3, 4)\)[/tex] on the graph as the solution to the system of equations.
By following these steps, you will successfully graph the system of equations and identify the point of intersection, which represents the solution to the system: [tex]\( x = -3 \)[/tex] and [tex]\( y = 4 \)[/tex].
### Task 1: Graph the Equations
#### Equation 1: [tex]\( 2x - 3y = -18 \)[/tex]
1. Convert to Slope-Intercept Form (y = mx + b):
[tex]\[ 2x - 3y = -18 \][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[ -3y = -2x - 18 \][/tex]
[tex]\[ y = \frac{2}{3}x + 6 \][/tex]
2. Plot the Line:
- Start by plotting the y-intercept ([tex]\( b \)[/tex]): [tex]\((0, 6)\)[/tex]
- Use the slope [tex]\( \frac{2}{3} \)[/tex] (rise over run):
- From [tex]\((0, 6)\)[/tex], move up 2 units and right 3 units to find another point, which gives you [tex]\((3, 8)\)[/tex].
- Draw the line passing through these points.
#### Equation 2: [tex]\( 3x + y = -5 \)[/tex]
1. Convert to Slope-Intercept Form (y = mx + b):
[tex]\[ 3x + y = -5 \][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[ y = -3x - 5 \][/tex]
2. Plot the Line:
- Start by plotting the y-intercept ([tex]\( b \)[/tex]): [tex]\((0, -5)\)[/tex]
- Use the slope [tex]\( -3 \)[/tex] (rise over run):
- From [tex]\((0, -5)\)[/tex], move down 3 units and right 1 unit to find another point, which gives you [tex]\((1, -8)\)[/tex].
- Draw the line passing through these points.
### Task 2: Determine the Solution
The solution to the system of equations is the point where the two lines intersect.
- Intersection Point: Observe the graph to find the coordinates where the two lines cross.
Given the solution to the system is:
[tex]\[ x = -3, \quad y = 4 \][/tex]
### Task 3: Plot the Solution
Using the Mark Feature tool:
- Mark the point [tex]\((-3, 4)\)[/tex] on the graph as the solution to the system of equations.
By following these steps, you will successfully graph the system of equations and identify the point of intersection, which represents the solution to the system: [tex]\( x = -3 \)[/tex] and [tex]\( y = 4 \)[/tex].
