Question

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

Answer 1

`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!