# Solve the system by graphing.

3x+y=6
3x-y=0

I'm kind of unsure about how to do this. I'm thinking I just put any point in for x and then solve for y...is that right?

you could let y=3x then substitute this value of y to the first equation...3x+3x=6 so, evaluating this... you get 6x=6 and your value for x would be 1 and substituting x=1 to y=3x, you get y=3*1

## To solve the system of equations 3x+y=6 and 3x-y=0 by graphing, you start by rewriting each equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

For the first equation, 3x+y=6, subtract 3x from both sides to isolate y:
y = -3x + 6

For the second equation, 3x-y=0, add 3x to both sides and rearrange to isolate y:
y = 3x

Now we have the two equations in slope-intercept form:
y = -3x + 6
y = 3x

To graph these equations, start by plotting the y-intercept for each equation. In the first equation, y = -3x + 6, the y-intercept is 6, so plot the point (0, 6) on the graph. In the second equation, y = 3x, the y-intercept is 0, so plot the point (0, 0) on the graph.

Next, use the slope of each equation to find additional points to plot. For the first equation, the slope is -3, which means that for every increase of 1 in x, y decreases by 3. So, starting from the y-intercept (0, 6), you can move down 3 units and to the right 1 unit to plot another point (1, 3). Repeat this process to find additional points.

For the second equation, the slope is 3, which means that for every increase of 1 in x, y increases by 3. Starting from the y-intercept (0, 0), move up 3 units and to the right 1 unit to plot another point (1, 3). Again, repeat this process to find more points.

After plotting the points for each equation, you will notice that they intersect at the point (1, 3). This means that the values of x and y that satisfy both equations are x = 1 and y = 3.

So, the solution to the system of equations 3x+y=6 and 3x-y=0 is x = 1 and y = 3.

## To solve the system by graphing, you will need to plot the equations on a graph and find the point of intersection. Here's how you can do it step by step:

1. Start by converting both equations to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Equation 1: 3x + y = 6
Rearrange to get: y = -3x + 6

Equation 2: 3x - y = 0
Rearrange to get: y = 3x

2. Now that both equations are in slope-intercept form, you can identify the slopes and y-intercepts.

Equation 1: Slope = -3, y-intercept = 6
Equation 2: Slope = 3, y-intercept = 0

3. Plot the lines on a graph using the slope and y-intercept values.

For the first equation: Start at the y-intercept of 6 and then use the slope -3 (rise -3, run 1) to find the second point. Connect the dots to form a line.

For the second equation: Start at the y-intercept of 0 and then use the slope 3 (rise 3, run 1) to find the second point. Connect the dots to form a line.

4. Find the point of intersection between the two lines. This point represents the solution to the system of equations.

In this case, the lines intersect at (1, 3). Therefore, the solution to the system is x = 1 and y = 3.

Graphing systems of equations can be a visual and intuitive way to solve them. However, keep in mind that it may not always provide an exact solution and can be subject to errors in reading the graph. For more accurate and precise solutions, other methods like substitution or elimination may be preferred.