What are the coordinates of the point of intersection of the following lines? 3x + 2y = 4 x + 3y = -1

Question

BlackTom AI · Accepted Answer

Use substitution from the second equation: x + 3y = −1 so x = −1 − 3y.

Substitute into 3x + 2y = 4:
3(−1 − 3y) + 2y = 4
Expand: −3 − 9y + 2y = 4
Combine like terms: −3 − 7y = 4
Isolate y: −7y = 4 + 3 = 7
So y = 7 / (−7) = −1.

Now find x using x = −1 − 3y:
x = −1 − 3(−1) = −1 + 3 = 2.

Thus the intersection point is (2, −1). Check by substituting into the first equation: 3(2) + 2(−1) = 6 − 2 = 4 (correct), and into the second: 2 + 3(−1) = 2 − 3 = −1 (correct).

Why the other options are incorrect:
- a. (1, −3): 3(1) + 2(−3) = 3 − 6 = −3 ≠ 4, so fails the first equation.
- b. (0, −2): 3(0) + 2(−2) = −4 ≠ 4, so fails the first equation.
- c. (3, −8): 3(3) + 2(−8) = 9 − 16 = −7 ≠ 4, so fails the first equation.
- d. (2, −1): satisfies both equations as shown.

Conclusion: the coordinates of the intersection are (2, −1), which matches the provided correct answer d. (2, −1).

What are the coordinates of the point of intersection of the following lines? 3x + 2y = 4 x + 3y = -1Single choice

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