I AM TRYING TO SOLVE A SYSTEM OF EQUATIONS BY GRAPHING AND CAN GET THIS ONE.

3x + y = 2
4y = 12 - 12x

HOW DO YOU DO THIS?

To solve the system of equations by graphing, we need to plot the graphs of both equations on a coordinate plane and find their point of intersection. The point of intersection represents the solution to the system.

Let's solve the system step-by-step:

1. Convert both equations to slope-intercept form, y = mx + b, where m represents the slope, and b represents the y-intercept.

Equation 1: 3x + y = 2
Rearrange the equation to solve for y:
y = -3x + 2

Equation 2: 4y = 12 - 12x
Divide both sides by 4:
y = -3x + 3

2. Now that we have the slope-intercept form of both equations, we can plot the graphs on a coordinate plane.

For equation 1 (y = -3x + 2), when x = 0, y = 2. Plot the point (0, 2) on the y-axis.

For equation 2 (y = -3x + 3), when x = 0, y = 3. Plot the point (0, 3) on the y-axis.

Using the slopes of both equations (-3), plot more points on each line using the respective slopes.

3. Draw the lines through the plotted points. The point where the lines intersect is the solution to the system of equations.

In this case, you will find that the two lines are parallel and will not intersect. Thus, there is no solution to this system of equations.

To confirm this algebraically, we can substitute the values of x and y from one equation into the other equation. If they do not satisfy the other equation, there is no solution.

To solve a system of equations by graphing, you need to plot the equations on a coordinate plane and find the point(s) where the graphs intersect. Here's how you can solve the given system of equations:

1. Start by expressing both equations in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept:

Equation 1: 3x + y = 2 => y = -3x + 2
Equation 2: 4y = 12 - 12x => y = -3x + 3

2. Now, graph each equation on the same coordinate plane. To do this:
- Pick a range for the x-axis (e.g., -5 to 5) and substitute different x-values into each equation to find corresponding y-values.
- Plot the points obtained and connect them to form a straight line for each equation.

3. The point(s) where the two lines intersect represent the solution(s) to the system of equations. If the lines do not intersect or are parallel, there is no solution.

In the case of the given system of equations:
- The first equation, y = -3x + 2, has a y-intercept of 2 and a slope of -3. Starting at (0, 2), you can use the slope to plot additional points and draw a line.
- The second equation, y = -3x + 3, has a y-intercept of 3 and a slope of -3. Again, starting at (0, 3), plot additional points using the slope and draw the line.

4. Once you have graphed both equations, identify the point where the lines intersect. This point represents the solution to the system of equations. If the lines do not intersect or are parallel, there is no solution.

Note: It is essential to be accurate when plotting points and drawing lines, as small errors can affect the accuracy of the solution.

Graph each Eq; the point where they intersect is the solution. Then verify

your solution by solving them mathematically.

Eq1: 3x + y = 2.
(-2,8), (0,2), (2,-4).

Eq2: 12x + 4y = 12.
Divide both sides by 4:
3x + y = 3.
(-2,9), (0,3), (2,-3).

Use the points given or any convenient points.

NOTE: The 2 Eqs have equal slopes. Therefore, they do not intersect and
there are no solution. Be sure to do
the graphs anyway.

m1 = -A/B = -3/1 = -3.
m2 = -A/B = -3/1 = -3.