Equations and Inequalities Chapter 1

Questions and Answers

What is the solution to the equation $3 - t = 3$?

t = 0

What is the solution to the equation $25 + 3t = 36$?

t = 11/3 or approximately 3.67

What is the relationship established from the equations $3x - y = 3$ and $9x - 3y = 9$?

They are equivalent equations.

What value of $x$ can be substituted in the equation $9(3 + y/3) - 3y = 9$?

<p>x = (13 - 3y)/2</p> Signup and view all the answers

What is the first equation to solve in the system of equations $0.2x + 0.3y = 1.3$ and $0.4x + 0.5y = 2.3$?

<p>0.2x + 0.3y = 1.3</p> Signup and view all the answers

Study Notes

Solving Equations Overview

Two types of equations presented: linear equations and equations with variables to solve.
Solutions involve isolating variables and substitution to test compatibility.

Part (i)

First equation: (3 - t = 3)
- Rearranged to find (t): (t = 0).
Second equation: (25 + 3t = 36)
- Rearrangement leads to (3t = 11) or (t = \frac{11}{3}), indicating potential contradiction.

Part (ii)

Given linear equations:
- First: (3x - y = 3)
- Second: (9x - 3y = 9), which simplifies to (3x - y = 3) showing both equations represent the same line.
Since both equations are equivalent:
- Infinite solutions exist; any (x) can yield (y) values based on the relationship (y = 3x - 3).

Part (iii)

Two equations presented to find (x) and (y):
- First: (0.2x + 0.3y = 1.3)
  - Multiplying through by 10 gives (2x + 3y = 13) for simplicity.
- Second: (0.4x + 0.5y = 2.3)
  - Multiplying through by 10 gives (4x + 5y = 23).
Find (x) from the first equation, expressed as ((13 - 3y)/2).
Both equations provide relationships to find specific values for (x) and (y).

Simplification Techniques

Substitute derived values into other equations to check for consistency.
Rearranging terms helps isolate variables for easier computation.
Identifying relationships between equations can aid in finding infinite solutions.

Description

Test your skills on solving various types of equations with this quiz. You will encounter linear equations with single variables, as well as systems of equations. Challenge yourself and see how well you can manipulate and solve these mathematical problems!