The solution to the system of equations x + 3y = 6 and 4x - 6y = 6 is x = 3 and y = 1.
Given the system of equations in the question:
x + 3y = 6
4x - 6y = 6
To solve the system of equations by graphing, firstly, graph equation on the graph and take the point of intersection.
x+3y = 6
4x-6y=6
For equation 1)
x + 3y = 6
Reorder in slope intercept form:
y = (-1/3)x + 2
Now, plug in x=0 to determine the y-intercept:
y = 0 + 2
y = 2
Plug in y = 3:
3 = (-1/3)x + 2
-x/3 = 3 - 2
x = -3
Now, plot the first line using the points (0,6) and (-3,3).
For the second equation:
4x - 6y = 6
Solve for y:
6y = 4x - 6
y = (2/3)x - 1
Now, plug in x = 0 to determine the y-intercept:
y = 0 - 1
y = -1
Plug in y = 3
3 = (2/3)x - 1
3 + 1 = 2x/3
2x/3 = 4
2x = 4 × 3
2x = 12
x = 12/2
x = 6
Now, plot the second line using the points (0,-1) and (6,3).
From the graph, the point of intersection is (3,1).