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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We are given two lines: 4x + 3y = 11 and 3x − 4y = 27.

To find their intersection, we solve the system for x and y.

One approach is elimination. Multiply the first equation by 4 to align the y-terms with opposite signs after combining: 4*(4x + 3y) = 4*11 gives 16x + 12y = 44.
Multiply the second equation by 3: 3*(3x − 4y) = 3*27 gives 9x − 12y = 81.
Now add the two new equations: (16x + 12y) + (9x − 12y) = 44 + 81, which simplifies to 25x = 125.
Solving for x yields x = 125 / 25 = 5.

Next, substitute x = 5 into one of the original equations to solve for y. Using 4x + 3y = 11: 4*(5) + 3y = 11 becomes 20 + 3y = 11.
Then 3y = 11 − 20 = −9, so y = −9 / 3 = −3.

Thus the coordinates where the two lines intersect 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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