Math: 567ac7ab

ID: 567ac7ab 

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

Comment: Know how to generate either infinite solutions or no solution from a system of equations.

Method 1: Notice that the first equation has even numbers across the board. Divide out the greatest common factor, 2:

2x + 6y = 10

x + 3y = 5

For the second equation to generate no solution, the left-hand side will have to be identical to the above (or some multiple), but with a different outcome. Such lines would be parallel and thus never intersect. Answer choice (A) is the same line, but (B) is what we are looking for: the correct answer is (B).

Method 2: Plug in the equations to Desmos and examine the graph. Select the answer that creates a parallel line to the first one.

The blue line covers the red line, so there are infinite number of solutions to the system. The green line, however, is parallel, so the correct answer must be (B). The other lines clearly touch the original line, so they would each produce a single solution.

Method 3: Worst-case scenario, you can still test the answer choices one by one. Elimination should not prove too difficult. How about starting with (A)?

2x + 6y = 10

x + 3y = 5 --> 2x + 6y = 10 

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0 = 0

Because this will always be true, you know you are dealing with an infinite number of solutions. Move on to (B).

2x + 6y = 10 --> x + 3y = 5

x + 3y = -20

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0 = 25

This equation, on the other hand, will never be true, meaning that you have found the correct answer, (B). Testing either (C) or (D) would yield a single answer, as shown in the graph above, in method 2.