Give the coordinates of the point of intersections for the two lines:[math: 4x+3y=11] [math: 3x−4y=27] 3x-4y=27

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BlackTom AI · Accepted Answer

We begin by identifying that we need the intersection point of two lines given by the equations 4x + 3y = 11 and 3x - 4y = 27.

One standard approach is elimination: multiply the first equation by 4 to align the y-term with the second equation that has -4y, and multiply the second equation by 3 to align the y-term oppositely, then add.
- Multiply: (4x + 3y = 11) by 4 gives 16x + 12y = 44.
- Multiply: (3x - 4y = 27) by 3 gives 9x - 12y = 81.
Adding these two new equations eliminates y: (16x + 12y) + (9x - 12y) = 44 + 81, yielding 25x = 125, so x = 5.

With x found, substitute back into one of the original equations to solve for y. Using 4x + 3y = 11: 4(5) + 3y = 11, which is 20 + 3y = 11. Then 3y = -9, so y = -3.

Thus, the intersection point is (x, y) = (5, -3).

Verification step helps confirm accuracy: substitute (5, -3) into both equations.
- For 4x + 3y = 11: 4(5) + 3(-3) = 20 - 9 = 11, which matches.
- For 3x - 4y = 27: 3(5) - 4(-3) = 15 + 12 = 27, which also matches.

Therefore, the coordinates of the intersection point are (5, -3).

Give the coordinates of the point of intersections for the two lines:[math: 4x+3y=11] [math: 3x−4y=27] 3x-4y=27

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Give the coordinates of the point of intersections for the two lines:[math: 4x+3y=11] [math: 3x−4y=27] 3x-4y=27

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