<h3>Answer:</h3>
(x, y) = (-7, 3)
<h3>Explanation:</h3>
The idea of substitution is that you write an expression for one of the variables in terms of the other variable(s), then use that expression in the place of the variable in all the other equations.
Here, your first equation gives and expression for y in terms of x. Use that expression in place of y in the second equation.
... y = -x-4 . . . . your first equation, defining y
... -x +2(-x-4) = 13 . . . . the above expression for y is put where y was in the second equation
Now, this is solved like any one-variable equation.
... -x -2x -8 = 13 . . . . eliminate parentheses
... -3x = 21 . . . . . . . . collect terms, add 8
... x = -7 . . . . . . . . . . divide by -3
... y = -(-7) -4 = 7 -4 = 3 . . . . use the expression for y to find the value of y
The solution is (x, y) = (-7, 3).
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<em>Comment on substitution</em>
Substitution works the same in equations as it does anywhere else in life. (Perhaps the only difference is that in equations, the substituted quantity must be <em>exactly equal</em>.) For example, in many vending machines, a dollar can be substituted for 4 quarters, and vice versa. In cooking, a small egg plus some additional liquid can be substituted for a large egg (in many cases).
The idea is that if two things are declared equivalent, either can be used in place of the other. For solving equations, this is a useful way to reduce the number of variables in an equation.
