anthonytapias / dsc-2-13-05-lingalg-linear-equations-quiz-nyc-career-ds-102218

Systems of Linear Equations - Quiz

Introduction

Following scenarios present problems that can be solved as system of equations, while performing substitutions and eliminations as we saw in the previous lesson.

• Solve these problems by hand, showing all the steps to work out the unknown variable values
• Verify your answers by showing the calculated values satisfy all equations

Objectives

You will be able to:

• Describe a system of linear equations for solving simple analytical problems
• Solve a system of equations using elimination and substitution

Exercise 1

Joe paid 12 dollars for 4 cups of coffee and 4 cups of tea. 3 cups of coffee cost as much as 2 cups of tea.

What would be the total cost of 5 cups of coffee and 5 cups of tea ?

Solution

Let x be the unit price of coffee and y be the unit price of tea

# Your solution here 

Exercise 2

Jim has more money than Bob. If Jim gave Bob 20 dollars , they would have the same amount. While if Bob gave Jim 22 dollars, Jim would then have twice as much as Bob.

How much does each one actually have?

Solution

Let x be the amount of money that Jim has and y be the amount that Bob has.

# Your solution here 

Exercise 3

Mia has 30 coins, consisting of quarters (25 cents) and dimes (10 cents), which total to the amount 5.70 dollars.

How many of each does she have?

# Your solution here 

Level up - Optional

For more pratice with linear equations, Visit following links for more complex equations and online answers verification:

• https://www.transum.org/software/SW/Starter_of_the_day/Students/Simultaneous_Equations.asp?Level=6
• https://www.transum.org/software/SW/Starter_of_the_day/Students/Simultaneous_Equations.asp?Level=7

Summary

In this lesson, we saw how to solve linear equations by hand to find the co-efficient values. We shall now move forward to have a deeper look into vectors and matrices and how Python and Numpy can help us solve more complex equations in an analytical context.