Question

Consider the system of equations.

x + y = 5

2x - y = -2

23. Solve the system of equations by graphing.
24. Solve the system of equations using the
substitution method.
25. Which method do you prefer in this instance?
Explain.

Answer 1

23. (1, 4)

24. (1, 4)

25. graphing calculator

Explanation:

You want to solve this system of equations by graphing and by substitution.

• x + y = 5
• 2x -y = -2

23. Graphing

The graph of the system of equations is attached. The solution is ...

(x, y) = (1, 4)

24. Substitution

Using the second equation, we can write an expression for y:

y = 2x +2

Substituting that into the first equation gives ...

x + (2x +2) = 5

3x = 3 . . . . . . . . subtract 2

x = 1

Then ...

y = 2(1) +2 = 4

The solution is (x, y) = (1, 4).

25. Preference

We like the graphing calculator solution, as it gives the answer as quickly as we can type the equations.

If we were constrained to drawing the graph by hand, we would prefer the substitution solution.

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