Solve the simultaneous equations3a−2b= −7,4a−5b= 14.

Sure, let's solve these simultaneous equations step by step.

Step 1: Write down the equations:

3a - 2b = -7 ...(1)

4a - 5b = 14 ...(2)

Step 2: Multiply equation (1) by 5 and equation (2) by 2 to make the coefficients of b the same in both equations:

15a - 10b = -35 ...(3)

8a - 10b = 28 ...(4)

Step 3: Subtract equation (4) from equation (3) to find the value of a:

(15a - 8a) = -35 - 28

7a = -63

a = -63 / 7

a = -9

Step 4: Substitute a = -9 into equation (1) to find the value of b:

3(-9) - 2b = -7

-27 - 2b = -7

-2b = -7 + 27

-2b = 20

b = 20 / -2

b = -10

So, the solution to the simultaneous equations is a = -9 and b = -10.