Solve by graphing
3x+y=15
3x+y=6
To solve these equations by graphing, we need to find the points where the two lines intersect.
Let's start by graphing the first equation, 3x + y = 15:
Step 1: Write the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
3x + y = 15
y = -3x + 15
Step 2: Plot the y-intercept, which is the point (0, 15).
Step 3: Use the slope to find more points. Since the slope is -3, we can move from the y-intercept down 3 units and right 1 unit to get the point (1, 12).
Step 4: Connect the two points and draw a straight line.
Now let's graph the second equation, 3x + y = 6:
Step 1: Write the equation in slope-intercept form.
3x + y = 6
y = -3x + 6
Step 2: Plot the y-intercept, which is the point (0, 6).
Step 3: Use the slope to find more points. Since the slope is -3, we can move from the y-intercept down 3 units and right 1 unit to get the point (1, 3).
Step 4: Connect the two points and draw a straight line.
Now we have both lines graphed on the same coordinate plane. The point where the lines intersect is the solution to the system of equations.
In this case, the lines are parallel and do not intersect. Therefore, there is no solution to the system of equations.