Question

y=-x+4 and y=x-2
number of solutions :
explain:

y=3x+4 and y=x-2
number of solutions :
explain:

Answer 1

1) y = −x + 4 and y = x − 2
- Solve: −x + 4 = x − 2 → 4 + 2 = x + x → 6 = 2x → x = 3.
- Then y = 3 − 2 = 1.
- Number of solutions: 1 (the intersection point is (3, 1)).
- Reason: slopes are −1 and 1 (different), so the lines meet in exactly one point.

2) y = 3x + 4 and y = x − 2
- Solve: 3x + 4 = x − 2 → 3x − x = −2 − 4 → 2x = −6 → x = −3.
- Then y = −3 − 2 = −5.
- Number of solutions: 1 (the intersection point is (−3, −5)).
- Reason: slopes are 3 and 1 (different), so the lines intersect in exactly one point.

(For reference: if two lines have different slopes they intersect once; if slopes are equal and intercepts equal they coincide (infinitely many solutions); if slopes equal and intercepts different they are parallel (no solutions).)