Solve the system of equations by the elimination method. 7/4x + 1/2y= 33/2

9/16x - 7/4y = -141/8

x=6 y=12

Step-by-step explanation:

first, you have to make one of the coefficients of the variables to match up but with opposite signs. in this problem, i will start by eliminating the y term

7/2(7/4x+1/2y=33/2) -> 49/8x+7/4y=231/4

49/8 is the same as 98/16, which i will use so there is a common denominator. 231/4 is the same as 462/8, which i use for the same reason

98/16x+7/4y=462/8

9/16x-7/4y=-141/8 (eliminate the y factor by adding the equations together)

107/16x=321/8 (divide these by multiplying by the reciprocal)

x=(321/8)(16/107) (multiply)

x=642/107 (simplify)

x=6

next, plug in this x factor in an equation to get the y factor.

7/4(6)+1/2y=33/2 (multiply)

21/2+1/2y=33/2 (subtract)

1/2y=6 (multiply)

y=12

hope this helps!