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What is the point of intersection when the line 2x -3y plus 5 equals 0 crosses the line 4x plus 5y -1 equals 0 on the Cartesian plane?
Wiki User
∙ 7y ago
You have two simultaneous equations; solve them:
- 2x - 3y + 5 = 0→ 2x - 3y = -5
- 4x + 5y - 1 = 0 → 4x + 5y = 1
As in the second equation the x coefficient is twice that in the first equation, subtract twice the first equation from the second and solve for y; {2}-2×{1}:
(4x - 2×2x) + (5y - 2×-3y) = 1 - 2×-5
→ (4x - 4x) + (5y - -6y) = 1 - -10
→ 5y + 6y = 1 + 10
→ 11y = 11
→ y = 1
Now substitute back into one of the equations (say {2}):
4x + 5y = 1
→ 4x + 5×1 = 1
→ 4x = 1 - 5 = -4
→ x = -1
Now substitute the values for x and y back into the other equation ({1}) as a check:
2x - 3y = 2×-1 - 3×1 = -2 - 3 = -5 as required.
Thus the lines intersect at the point (-1, 1).
Wiki User
∙ 7y ago
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