Solve the simultaneous equations6x+7y= 9,3x+8y= −9.

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

Step 1: Write down the equations:

6x + 7y = 9 ---- (1)

3x + 8y = -9 ---- (2)

Step 2: To eliminate one of the variables, we can multiply the entire equation (2) by 2. This gives us:

6x + 16y = -18 ---- (3)

Step 3: Now, subtract equation (3) from equation (1):

6x + 7y - (6x + 16y) = 9 - (-18)

This simplifies to:

-9y = 27

Step 4: Solve for y by dividing both sides by -9:

y = 27 / -9

y = -3

Step 5: Substitute y = -3 into equation (1):

6x + 7(-3) = 9

6x - 21 = 9

6x = 30

Step 6: Solve for x by dividing both sides by 6:

x = 30 / 6

x = 5

So, the solution to the simultaneous equations is x = 5 and y = -3.