Question

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

x + y = 1
2x – 3y = –30

Answer 1

x + y = 1.......multiply by -2
2x - 3y = -30
----------------
-2x - 2y = -2 (result of multiplying by -2)
2x - 3y = -30
---------------add
-5y = -32
y = 32/5 or 6 2/5 <===

Answer 2

Answer: The required value of y in the solution to the given system is 6.4.

Step-by-step explanation: We are given to find the value of y in the solution to the following system of linear equations :

`x+y=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-3y=-30~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

To find the value of y, we will try to eliminate x from both the equations.

Multiplying equation (i) by 2, we have

`2(x+y)=1*2\\\\\Rightarrow 2x+2y=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Subtracting equation (ii) from equation (iii), we get

`(2x+2y)-(2x-3y)=2-(-30)\\\\\Rightarrow 2y+3y=2+30\\\\\Rightarrow 5y=32\\\\\Rightarrow y=(32)/(5)\\\\\Rightarrow y=6.4.`

Thus, the required value of y in the solution to the given system is 6.4.