What values of 𝑥x and 𝑦y make both of these equations true? 2𝑦2y==𝑥+6x+6𝑦−3𝑥y−3x==33

The equations you provided are:

1. 2y = x + 6
2. y - 3x = 3

Let's solve these equations step by step:

Step 1: Rearrange the first equation to solve for x.

x = 2y - 6

Step 2: Substitute x in the second equation with the expression we found in step 1.

y - 3(2y - 6) = 3 y - 6y + 18 = 3 -5y + 18 = 3 -5y = 3 - 18 -5y = -15 y = -15 / -5 y = 3

Step 3: Substitute y = 3 into the first equation to solve for x.

2*3 = x + 6 6 = x + 6 x = 6 - 6 x = 0

So, the solution to the system of equations is x = 0 and y = 3.