𝑀 is the point of intersection of the lines with equations 4𝑥+3𝑦=17 and 5𝑥−4𝑦=−17.5Write down the coordinates of 𝑀.

To find the point of intersection M of the two lines, we need to solve the system of equations given by the two lines. The system of equations is:

4x + 3y = 17 5x - 4y = -17.5

Step 1: Multiply the first equation by 4 and the second equation by 3 to make the coefficients of y the same in both equations:

16x + 12y = 68 15x - 12y = -52.5

Step 2: Add the two equations together:

16x + 15x = 68 - 52.5 31x = 15.5

Step 3: Solve for x:

x = 15.5 / 31 x = 0.5

Step 4: Substitute x = 0.5 into the first equation:

4(0.5) + 3y = 17 2 + 3y = 17 3y = 15 y = 15 / 3 y = 5

So, the point of intersection M of the two lines is (0.5, 5).