How do solve the following linear system?: 3/2x - 3y = -9/4 , 5x+2y=1 ?

1 Answer
jim p.
Sep 20, 2017

x = -1/12

y = 17/24

Explanation:

Multiply through by 2 in the first equation, giving:

3x - 6y = -9/2

Multiply through by 3 in the second equation, giving:

15x + 6y = 3#

...now add the two equations, which allows you to elimintate the y variable:

18x = 3 - 9/2 = 6/2 - 9/2 = -3/2

x = -3/(2 * 18) = -1/12

...once we know x, we can plug back into either of the initial equations and solve for y:

5(-1/12) + 2y = 1
2y = 1 + 5/12 = 17/12

y = 17/24

SANITY CHECK - we used the second equation to solve for y. Let's plug both our calculated values back into the first equation to double check that the solutions satisfy both equations:

3/2(-1/12) -3(17/24) =

(-3 - 51)/24 = -54/24 = -9/4 CHECK!

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