Question

Solve the system of equations and choose the correct answer from the list of options. d + e = 1 −d + e = −5 Label the ordered pair as (d, e). (4 points) a (0, 0) b (3, −2) c (−2, 3) d (−3, 0)

Answer 1

b (3, −2)

Explanation:

You want the solution to the system of equations ...

• d +e = 1
• -d +e = -5

Elimination

We see the coefficients of d are opposites, so we can add the equations together to eliminate the d variable:

(d +e) +(-d +e) = (1) +(-5)

2e = -4 . . . . . . . . simplify

e = -2

Substituting into the first equation, we have ...

d +(-2) = 1

d = 3 . . . . . . add 2

The solution is (d, e) = (3, -2).

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Additional comment

We also note that the coefficients of 'e' are identical, so we can eliminate 'e' as a variable by subtracting one equation from the other. We choose to subtract the equation with the lower value coefficient of 'd'.

(d +e) -(-d +e) = (1) -(-5)

2d = 6 . . . . . . . simplify

d = 3 . . . . . . . . divide by 2; matches the solution above.

The attached graph uses x and y, because those are the built-in independent and dependent variables. Your graphing calculator may let you define the variables as you wish.