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 :
[tex]x+y=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-3y=-30~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
To find the value of y, we will try to eliminate x from both the equations.
Multiplying equation (i) by 2, we have
[tex]2(x+y)=1\times2\\\\\Rightarrow 2x+2y=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Subtracting equation (ii) from equation (iii), we get
[tex](2x+2y)-(2x-3y)=2-(-30)\\\\\Rightarrow 2y+3y=2+30\\\\\Rightarrow 5y=32\\\\\Rightarrow y=\dfrac{32}{5}\\\\\Rightarrow y=6.4.[/tex]
Thus, the required value of y in the solution to the given system is 6.4.
