Which expression could be substituted for y in the first equation to find the value, given the system of equations: 3x - 2y = 0 and 3x + 3y = 33?
Understand the Problem
The question requires determining which expression can be substituted for 'y' from the second equation (3x + 3y = 33) into the first equation (3x - 2y = 0). This involves isolating 'y' in the second equation and then presenting the resulting expression.
Answer
$-x + 11$
Answer for screen readers
-x+11
Steps to Solve
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Isolate the term with y in the second equation We start with the second equation: $3x + 3y = 33$. We want to isolate the term with $y$, so we subtract $3x$ from both sides: $3y = 33 - 3x$
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Solve for y Divide both sides of the equation by 3 to isolate $y$: $y = \frac{33 - 3x}{3}$
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Simplify the expression for y Divide each term in the numerator by 3: $y = \frac{33}{3} - \frac{3x}{3}$ $y = 11 - x$ Which can also be written as $y = -x + 11$
-x+11
More Information
The expression $-x + 11$ is obtained by isolating 'y' in the equation $3x + 3y = 33$ and simplifying. This expression can then be substituted into the first equation, $3x - 2y = 0$, to solve for the value of 'x'.
Tips
A common mistake is not distributing the division correctly when simplifying the expression for $y$. For example, some might incorrectly simplify $\frac{33 - 3x}{3}$ to $33 - x$.
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