Draw the pair, read the crossing
A picture can solve a pair. You draw both lines and read the point they share.
2x + y = 8. Two points are (0, 8) and (4, 0). Join them. Step 1 of 4
- Line 1 is
2x + y = 8. Two points are (0, 8) and (4, 0). Join them. - Line 2 is
x − y = 1. Two points are (1, 0) and (4, 3). Join them. - The lines cross at (3, 2). That point is on both lines.
- Check it in both.
2 × 3 + 2 = 8and3 − 2 = 1.
The rule
Find two points on each line. Join them. Read where they cross.
Two points are enough, because two points fix one straight line. Choose an easy x. Then find y from the equation. The crossing is on both lines. So it fits both equations.
| Line | Choose x | Find y | Point |
|---|---|---|---|
2x + y = 8 | 0 | y = 8 − 2 × 0 = 8 | (0, 8) |
2x + y = 8 | 4 | y = 8 − 2 × 4 = 0 | (4, 0) |
x − y = 1 | 1 | y = 1 − 1 = 0 | (1, 0) |
x − y = 1 | 4 | y = 4 − 1 = 3 | (4, 3) |
Read the picture
| The lines | Solutions | The pair is |
|---|---|---|
| cross at one point | exactly one: the point | consistent |
| run parallel | none | inconsistent |
| lie on each other | every point on the line | dependent, and consistent |
Now try it. Slide x until the two dots meet.
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