Question

Unit 5: systems of equations and inequalities Homework 3: Solving systems by elimination (All Things Algebra®, LLC)

Answer 1

(x, y) = (-3, -5)

Explanation:

You want to solve the given system of equations by elimination.

• 2x -3y = 9
• -5x -3y = 30

Elimination

To eliminate a variable from the equations, we need to add them in such a way that the coefficients for one of the variables have a total of zero.

Here, we observe that the y-coefficients are the same, so subtracting one equation from the other will cancel the y-terms. We want the result of that subtraction to give an equation with x having a positive coefficient, so we elect to subtract the second equation from the first:

(2x -3y) -(-5x -3y) = (9) -(30)

7x = -21 . . . . . simplify (y-terms are gone, x-term has positive coefficient)

x = -3 . . . . . . . divide by 7

Substitution

The value of y can be found from either equation. We choose to use the first one:

2x -3y = 9

2(-3) -3y = 9 . . . . . . substitute -3 for x in the first equation

-15 = 3y . . . . . . add 3y-9

-5 = y . . . . . . . divide by 3

The solution is (x, y) = (-3, -5).