What values of 𝑥x and 𝑦y make both of these equations true? 2𝑦2y==𝑥+6x+6𝑦−3𝑥y−3x==33
Question
What values of 𝑥 and 𝑦 make both of these equations true?
Solution
The equations you provided are:
- 2y = x + 6
- 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.
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