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Sep 18, 2023



If 2x 3 2y= 5 2 and x 5 2y=3 , what is the value of y?

15 4

45 28


45 52

165 26

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Scott Scott Woodbury-Stewart Founder and Expert GMAT Instructor


While this is a system of two equations, we can apply the same strategy of clearing the fractions from each equation using the LCM. The first equation has denominators of 3 and 2. The multiples of 3 are 3, 6, …. The multiples of 2 are 2, 4, 6, …. Thus, we see that the LCM of 3 and 2 is 6. We can multiply the entire first equation by 6 and simplify:

6 2x 3 2y= 5 2 6 2 2x 3 6 2y = 6 3 5 2 2(2x)6(2y)=3(5) 4x12y=15

For the second equation, we see that the LCM of the denominators is the sole denominator, which is 5. Thus, we multiply the entire equation by 5 and simplify:

     5   x 5  2y=3        5x 5  5(2y)=5(3)     x10y=15     

To determine the value of y, we can solve the system of equations by using the substitution method. In order to do so, let’s isolate x in the second equation by adding 10y to both sides:


We can now substitute 10y + 15 for x in the first equation:

     4x12y=15     4(10y+15)12y=15     40y+6012y=15     28y=45     y=  45  28      
Correct answer: B

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