Answer:
-10
Step-by-step explanation:
You are asked to tell the y-value of the solution. You can find the whole solution and then report the y-value, or you can just find the y part of the solution. We choose the latter.
This is basically done by eliminating the x-variable. It can be done using the "elimination" method of solving these equations. And it can also be done using the "substitution" method of solving these equations. We choose the latter.
Add 14 to the second equation to solve for x:
... x = y + 14
Substitute this into the first equation.
... 3(y +14) -y = 22
... 2y +42 = 22 . . . . . . simplify
... y +21 = 11 . . . . . . . . divide by 2
... y = -10 . . . . . . . . . . subtract 21
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<em>Comment on additional solution methods</em>
A graphing calculator can show you the solution, as in the attachment. Of the solution (x, y) = (4, -10), we are only interested in y = -10.
Cramer's rule can find just one variable value, too. For that, it is convenient to write the system as ...
- 3x -y = 22
- x - y = 14 . . . . . add 14-y to the equation given
Then the solution for y is ...
... y = (22·1 -14·3)/(-1·1 -(-1)·3) = -20/2 = -10
