Question

What is the value of y in the solution to the system of equations? 1x + 1y = 1 2x – 3y = -30​

Answer 1

Answer:

y=8

Step-by-step explanation:

$\frac{1}{3} x + \frac{1}{4}y= 1\\\\\frac{4x+3y}{12} =1\\4x+ 3y =12\\y = \frac{12-4x}{3}$

let's note this as our equation no. (i)

and let 2x-3y = -30 be the equation no. (ii)

Put value of y from (i) into (ii)

$2x -3y = -30\\2x-3(\frac{12-4x}{3} )=-30\\2x -12+4x = -30\\6x = -30+12\\6x= -18\\x = -3$

Now put x = -3 back in equation (i)

$y = \frac{12-4x}{3}\\y = \frac{12 - 4(-3)}{3}\\y = \frac{12 + 12}{3} \\y = 8$