Question

Consider the system of equations, y = f(x) and y= g(x), where

f(x) = 11x-7 and g(x) = 3x + 17.
Which method would you use to solve this system of equations? Explain
your reasoning and provide the solution to the system.

Answer 1

(x, y) = (3, 26)

Explanation:

I like to solve systems of equations like this by graphing. A graphing calculator easily shows the solution for both x and y.

(x, y) = (3, 26)

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As an alternative, here, the equations can be subtracted.

y = f(x)

y = g(x)

0 = f(x) - g(x) . . . . subtract the second equation from the first

0 = 11x -7 -(3x +17)

0 = 8x -24 . . . . simplify

0 = x -3 . . . . . . .divide by 8

3 = x

Now, we can substitute into either equation:

y = g(x) = 3(3) +17 = 26

The solution is (x, y) = (3, 26).