Question

12. The partial solution to a system of equations below contains an error. Find and correct the mistake to find the correct values of x and y. 2x – 3y =-6 5x + 3y = 27 steps1. 7x = 21 2. x = 3 3. 2 (3) – 3y = -6 4. 6 - 3y = -6 5. – 3y = - 12 6. y = - 4

Answer 1

The first step in solving this system is adding the two equations. Doing this gives us

`(2x+5x)+(3y-3y)=27-6`
`7x=21`

So the first step is done correctly.

Solving the above equation gives us

`x=3\text{.}`

Step 2 looks fine as well.

Now we use this x value to solve for y.

For that, we use the first equation 2x-3y=-6. Putting in the value of x gives

`2(3)-3y=-6`

that's step 3 which we now know is also right. We simplify further

`6-3y=-6`

step 4 is also right.

Subtract 6 from both sides and we get

`-3y=-12`

step 5 is also correct!

And finally, we divide both sides by -3 and get

`y=4`

Step 6 is wrong! Because it does not cancel the negative sign on both sides!

Hence, step 6 is wrong and the correct value of x and y is (x,y) = (3,4)