Answer:
(a) (5, -3)
Explanation:
The "substitution method" for solving a system of equations requires that you write an expression that can be substituted for a variable in one or more of the other equations in the system.
Expression to substitute
The given equations are ...
We notice the first equation gives an expression for y. This is exactly what we want to substitute for y in the second equation.
Substitution
When the expression (x-8) is substituted for y in the second equation, you get ...
2x +3(x -8) = 1
This simplifies to ...
5x -24 = 1
Solution
This 2-step equation can now be solved in the usual way:
5x = 25 . . . . . . add 24 to isolate the variable term
x = 25/5 = 5 . . . . . divide by the coefficient of x
Note that we now know what the correct answer choice is.
Using the expression for y, we find ...
y = x -8 = 5 -8 = -3
The solution is (x, y) = (5, -3).
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The attached graph confirms this solution.