To solve the equations graphically, we first need to rearrange both equations in the slope-intercept form (y = mx + b) to easily plot them on a graph.
Starting with the first equation:
1. x + 3y = 6
Subtract x from both sides:
3y = 6 – x
Now, divide by 3:
y = 2 – (1/3)x
This equation has a y-intercept of 2 and a slope of -1/3.
2. 2x + 3y = 12
Subtract 2x from both sides:
3y = 12 – 2x
Now, divide by 3:
y = 4 – (2/3)x
This equation has a y-intercept of 4 and a slope of -2/3.
Next, we will plot both lines on a graph:
- The first line (y = 2 – (1/3)x) crosses the y-axis at (0, 2). With a slope of -1/3, it will go down one unit for every three units it moves to the right.
- The second line (y = 4 – (2/3)x) crosses the y-axis at (0, 4). With a slope of -2/3, it will go down two units for every three units it moves to the right.
By graphing these two lines, we will look for the point where they intersect. The solution to the system of equations occurs at this intersection point, which gives us the values of x and y that satisfy both equations.
Upon plotting the lines, you should find that they intersect at the point (x, y). This point is the solution to the equations.