Question

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

3x + y = 14

-3x + 2y = 1

Answer 1

y=5

Answer 2

More generally, you have two equations:\[3x+y=14,\]\[-3x+2y=1.\]Pick any of those two equations, and pick any of the two variables: Let's pick the first equation and the variable \(y\).
Now, let's solve for \(y\):\[y=14-3x.\]We now take this equation, substitute it into the second one, and simplify, like this:\[-3x+2(14-3x)=1,\]\[-3x+28-6x=1,\]\[-9x=-27,\]\[x=3.\]We now know what the value of \(x\) is, so we plug it into any of the two original equations above to find \(y\): Let's pick the first equation, again:\[3(3)+y=14,\]\[9+y=14,\]\[y=5.\]Finally, the point \((x,y)\) which solves the above system is \((3,5)\), proving Jetly's answer.