Math: f718c9cf

ID: f718c9cf 

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)

Comment: Graphing is probably the fastest way to solve this one, since the x- and y-coordinates at the point of intersection will be shown directly, leaving only the multiplication at the end.

Method 1: It might seem by the book, but in a system of linear equations, either substitution or elimination will work. I prefer elimination more often than not, especially when it is easy to multiply one equation to get the coefficients of one variable or another to match.

2(5x + 14y = 45) --> 10x + 28y = 90

10x + 7y = 27

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21y = 63

y = 3

10x + 7(3) = 27

10x + 21 = 27

10x = 6

x = 6/10, 3/5 when reduced, or 0.6

xy = (0.6)(3) = 1.8

The answer is 1.8 or 9/5. 

Method 2: Plug in the equations to Desmos. The point of intersection of the two lines is (0.6, 3). Start another line to multiply these numbers to get the answer. If you type at a reasonable rate, this solution might take 30-45 seconds.

The answer, 1.8, is fine as a decimal.

Method 3: You could also use substitution to tackle this system of equations. If you had gotten unlucky and solved for x first, the question might take a bit more time to work out, since x is not an integer. As long as you are working toward a solution, though, it is worth moving forward. This time, I will eliminate y first.

5x + 14y = 45

2(10x + 7y = 27) --> 20x + 14y = 54

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-15x = -9

x = 9/15, 3/5 when reduced, or 0.6

10(3/5) + 7y = 27

6 + 7y = 27

7y = 21

y = 3

xy = (3/5)(3) = 9/5 or 1.8