Answer:
(x, y) = (-3, -5)
Explanation:
Substitution works in equations the same way it works in real life. Things that are equal can be used to replace one another.
When solving equations by substitution, the idea is to write an expression for one of the variables in terms of the other variable(s) in the problem. Substituting the expression for the variable will reduce the number of variables in the problem. Repeating this process as necessary can eventually reduce the problem to a single equation in a single variable, which we expect to know how to solve
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The second equation is suitable for writing a substitution expression after we remove the common factors of 9:
x - y = 2 . . . . . second equation, both sides divided by 9
x = y +2 . . . . . add y to both sides
Now, we can substitute this expression into the first equation:
7(y +2) -8y = 19 . . . . . . put (y+2) in place of x
-y +14 = 19 . . . . .simplify
y = -5 . . . . . . . . . add y-19 to both sides
Using the above expression for x, we find ...
x = (-5) +2 = -3
The solution is (x, y) = (-3, -5).
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We show a graphing calculator solution as a check on our answer.