Question

Solve by graphing:

6x + 3y = 12

8x + 4y = 24

Answer 1

To graph the system of equations, we will first rewrite both equations in slope-intercept form (y = mx + b).

For equation 1, 6x + 3y = 12, we isolate y:
3y = -6x + 12
y = -2x + 4

For equation 2, 8x + 4y = 24, we isolate y:
4y = -8x + 24
y = -2x + 6

Now we can plot the graphs of both equations:

Equation 1: y = -2x + 4
The y-intercept is 4 and the slope is -2, so we can plot a point at (0, 4) and use the slope to find other points:
-2/1 = the change in y / the change in x
Starting at (0, 4), we can move down 2 units and to the right 1 unit to find another point: (1, 2).

Equation 2: y = -2x + 6
The y-intercept is 6 and the slope is -2, so we can plot a point at (0, 6) and use the slope to find other points:
-2/1 = the change in y / the change in x
Starting at (0, 6), we can move down 2 units and to the right 1 unit to find another point: (1, 4).

Now we can graph both lines on the same coordinate plane:

The line for equation 1 is the green line:
{{{graph(300,300,-5,5,-5,10,-2x+4)}}}

The line for equation 2 is the blue line:
{{{graph(300,300,-5,5,-5,10,-2x+6)}}}

By looking at the graph, we can see that the lines intersect at the point (2, 0). Therefore, the solution to the system of equations is x = 2 and y = 0.