Find the solution to the system: y = 3x − 4 and y = −x + 2.

Correct — C. Both equations give y, so set the right-hand sides equal.

3x − 4 = −x + 2
Add x to both sides: 4x − 4 = 2
Add 4: 4x = 6
Divide by 4: x = 1.5

Substitute into y = −x + 2: y = −1.5 + 2 = 0.5
Check in y = 3x − 4: 4.5 − 4 = 0.5 ✓

The lines meet at (1.5, 0.5) → option (c)

Why the others are wrong

• (a)
  (1, −1) — (1, −1) fits y = 3x − 4, since 3 − 4 = −1, but fails y = −x + 2: −1 + 2 = 1, not −1. It lies on the first line only.
• (b)
  (0, 2) — (0, 2) is where y = −x + 2 crosses the y-axis. In y = 3x − 4, x = 0 gives y = −4, not 2, so the point is not on the first line.
• (d)
  (1.5, −3.5) — (1.5, −3.5) has the right x but the wrong y: at x = 1.5 both lines give 0.5. Writing −1.5 − 2 instead of −1.5 + 2 is what produces −3.5.

A system's solution is the point that satisfies both equations at once: the point where the two lines cross.

The slopes here are 3 and −1. Different slopes mean the lines are not parallel, so they meet at exactly one point.

When both equations already read y = …, setting them equal removes y in one step.

Key facts

• A solution of a system must satisfy every equation in it.
• Lines y = m₁x + c₁ and y = m₂x + c₂ with m₁ ≠ m₂ meet at exactly one point.
• Equal slopes with different intercepts give parallel lines and no solution.

Common traps

• Testing an option in one equation only: (1, −1) passes y = 3x − 4 and (0, 2) passes y = −x + 2.
• Stopping at x = 1.5: options (c) and (d) share that x, so the y has to be worked out and checked.

No directly related past PYQ was found.