Question

Solve graphically:

x + 3y = –2, 2x – y = 3

Answer 1

1. Rearrange to slope-intercept form

To graph the lines, we first rewrite each equation in the form y = mx + c:

Equation 1: x + 3y = –2

Subtract x from both sides: 3y = –x – 2

Divide by 3: `y = -1/3 x - 2/3`

Equation 2: 2x – y = 3

Subtract 2x from both sides: –y = –2x + 3

Multiply by –1: y = 2x – 3

2. Find plotting points

Next, calculate a few (x, y) coordinates for each line to plot them on a cartesian plane:

For x + 3y = –2:

If x = –2, then y = 0

⇒ (–2, 0)

If x = 1, then y = –1 

⇒ (1, –1)

If x = 4, then y = –2

⇒ (4, –2)

For 2x – y = 3:

If x = 0, then y = –3

⇒ (0, –3)

If x = 1, then y = –1

⇒ (1, –1)

If x = 2, then y = 1

⇒ (2, 1)

3. Plot and Find the intersection

Plot the coordinates found in Step 2 on a graph and draw a straight line through each set of points.

As shown in the graph, the two lines intersect at exactly one point. This point of intersection represents the values of x and y that satisfy both equations simultaneously.

The point of intersection is (1, –1), therefore the solution is x = 1 and y = –1.