Question

What is the value of y in the solution to the system of equations?

1/3x + 1/4y =1
2X - 3y = -30
A. -8
B. -3
C. 3
D. 8

Answer 1

D. 8

Explanation:

Given system of equations:

`\begin{cases}(1)/(3)x+(1)/(4)y=1\\\\2x-4y=-30\end{cases}`

Multiply the first equation by -6:

`\implies -6 \cdot (1)/(3)x+-6 \cdot (1)/(4)y=-6 \cdot 1`

`\implies -2x-(3)/(2)y=-6`

Add this to the second equation to eliminate x:

`\begin{array}{rrcccl}&2x &- &3y& = &-30\\\phantom{\frac12}+ &(-2x& - &(3)/(2)y &= &\;\;-6)\\\cline{2-6} \phantom{\frac12}&0&-&(9)/(2)y&=&-36\\ \cline{2-6}\end{array}`

Solve the equation for y:

`\implies -(9)/(2)y=-36`

`\implies (9)/(2)y=36`

`\implies 9y=72`

`\implies y=(72)/(9)`

`\implies y=8`