Question 1

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

Accepted Answer

Plot each equation for y, find the intersection point, and use its coordinates as the solution.

Question 2

Given the system of equations $$x - y = 4$$ and $$x + y = 12$$, what is the solution for $$(x, y)$$?

Accepted Answer

$$(8, 4)$$

Question 3

When using the substitution method to solve a system of equations, what is the first step?

Accepted Answer

Solve one of the equations for one variable.

Question 4

Solve the system using the substitution method: $$3x + y = 8$$ and $$2y + 6x = 18. $$What is the value of $$y$$?

Accepted Answer

$$y = 2$$

Question 5

Which of the following is a key step in the elimination method for solving systems of equations?

Accepted Answer

Multiply one or both equations so that the coefficients of one variable are opposites.

Question 6

Solve the system using the elimination method: $$0.3x + 0.5y = 1.9$$ and $$0.5x + 0.3y = 2.1. $$What is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 7

If the graphs of two linear equations are the same line, what does this indicate about the system?

Accepted Answer

The system has infinitely many solutions.

Question 8

You invested $$8000 between two accounts paying 3% and 5% annual interest, respectively. If the total interest earned for the year was 340$$, how much was invested at each rate?

Accepted Answer

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

Question 9

The Coffee Crafter charges $$11 per pound for Kenyan French Roast coffee and 10 $$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 10

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

Accepted Answer

$$27 km/h$$

Question 11

A riverboat travels 54 km downstream in 2 hours. It travels 36 km upstream in 3 hours. What is the speed of the stream?

Accepted Answer

$$6 km/h$$

Question 12

If a system of equations has no solution, what does this mean about the graphs of the equations?

Accepted Answer

The lines are parallel and never intersect.

Question 13

Which method is most efficient for solving a system where one equation is already solved for a variable?

Accepted Answer

Substitution method

Question 14

What is the solution to the system $$x - y = 4$$ and $$x + y = 12$$ using the elimination method?

Accepted Answer

$$(8, 4)$$

Question 15

If you multiply both sides of an equation by 10 to clear decimals, which system is equivalent to $$0.3x + 0.5y = 1.9$$ and $$0.5x + 0.3y = 2.1$$?

Accepted Answer

$$3x + 5y = 19$$ and $$5x + 3y = 21$$

Solving Systems of Linear Equations: Methods and Applications

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