ID: 52cb8ea4
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)
Comment: Whenever a system of equations asks about some strange-looking sum or difference of x and y, there is almost always a direct pathway to the answer by adding or subtracting one equation from the other.
Method 1: If it seems odd that the question is asking about 3x + 3y, rather than, say, the value of x or y independently, then it is probably an idea worth exploring. Looking at the coefficients 7x and 4x provides a way to get directly to 3x, by subtraction; the same can be said of -5y and -8y, although this one may not be as apparent, since both terms are negative. There it is: simply subtract the second equation from the first and answer the question.
7x - 5y = 4
4x - 8y = 9
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3x + 3y = -5
The correct answer is (B).
Method 2: Plug in the equations to Desmos and graph. Highlight the point of intersection.
Method 3: You could use substitution or elimination as a general method to work through systems of equations, but here, that method can lead to a lot of extra work, and the greater the number of steps involved, especially with tricky fractions or decimals and negatives, the greater the probability of making a mistake. Say we decided to eliminate x:
4(7x - 5y = 4) --> 28x - 20y = 16
7(4x - 8y = 9) --> 28x - 56y = 63
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36y = -47
y = -47/36
Now, substitute this value into either equation to solve for x.
7x - 5(-47/36) = 4
7x + 235/36 = 4
36 * 7x + 235 = 4 * 36
252x = 144 - 235
252x = -91
x = -91/252
Thus, 3x + 3y will be
3(-91/252) + 3(-47/36)
-91/84 - 47/12
-91/84 - 329/84
-420/84
-5
The correct answer is (B).
This method is clearly labor- and time-intensive next to either of the two methods above, so I would not recommend it. However, should you find yourself starting a problem and running into some odd-looking numbers like the derived value of y, it is probably a hint that you are doing more work than you need to.
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