Question 1

Which of the following best describes the graphical method for solving a system of linear equations?

Accepted Answer

Solve each equation for $$y$$, plot both lines, and identify their intersection point.

Question 2

Given the system: $$x - y = 4$$ and $$x + y = 12$$, what is the solution using the substitution method?

Accepted Answer

$$x = 8, y = 4$$

Question 3

Which scenario indicates that a system of equations has no solution when using the graphical method?

Accepted Answer

The lines are parallel and never intersect.

Question 4

Solve the following system using the elimination method: $$2x + 6y = 18$$ and $$3x - y = 2.$$

Accepted Answer

$$x = 3, y = 2$$

Question 5

If you invest $$8000$$ between two accounts paying $$3\%$$ and $$5\%$$ annual interest, and the total interest earned after one year is $$340$$, how much was invested at each rate?

Accepted Answer

$$3000 at$$ $$3\%$$, $$5000 at$$ $$5\%$$

Question 6

A coffee grinder charges $$11$$ per pound for Kenyan French Roast and $$10$$ per pound for Sumatran coffee. How much of each type should be used to make a $$20-$$pound blend that sells for $$10.35$$ per pound?

Accepted Answer

$$7$$ pounds Kenyan, $$13$$ pounds Sumatran

Question 7

A riverboat travels $$54 km $$downstream in $$2$$ hours and $$36 km $$upstream in $$3$$ hours. What is the speed of the boat in still water?

Accepted Answer

$$21 km/h$$

Question 8

Which of the following is a necessary first step when using the substitution method to solve a system of equations?

Accepted Answer

Solve one equation for one variable in terms of the other.

Question 9

If the elimination method results in a false statement such as $$0 = 5$$, what does this indicate about the system?

Accepted Answer

The system has no solution.

Question 10

Given the system $$0.3x + 0.5y = 1.9$$ and $$0.5x + 0.3y = 2.1$$, what is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 11

Which of the following best describes a system of equations with infinitely many solutions?

Accepted Answer

The equations represent the same line.

Question 12

If you graph two equations and they intersect at $$(2, 5)$$, what does this point represent?

Accepted Answer

The solution to the system of equations.

Solving Systems of Linear Equations: Methods and Applications

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