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Maths Lesson 1: Linear Equations in Two Variables

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Maths Lesson 1: Linear Equations in Two Variables

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Questions and Answers

The equation 2x + 3y = 5 represents a straight line when graphed.

True

Which of the following is a linear equation in two variables?

5y - 2 = 0

3x + 4y = 12 (correct)

x^2 + y^2 = 9

y = 3y + 1

What is the solution of the equation 2x + 5 = 15?

In the equation 4x + 3y = 12, the value of x when y = 0 is _____

3 Signup and view all the answers

Match the following linear equations with their slopes:

y = 2x + 3 = 2 y = -3x + 4 = -3 y = 5 = 0 x + y = 7 = -1 Signup and view all the answers

What is the general form of a linear equation in two variables?

Ax + By = C Signup and view all the answers

Which of the following pairs of values (x, y) satisfy the linear equation 3x - 4y = 12?

(4, 0) Signup and view all the answers

What is the slope of the line represented by the equation 5y = 15 - 10x?

-2 Signup and view all the answers

If the linear equation is represented as 2x + 3y = 6, what is the y-intercept of the line?

3 Signup and view all the answers

Which of the following statements is true about the linear equation 7x + 2y = 14?

The relationship between x and y is linear. Signup and view all the answers

Study Notes

Linear Equations in Two Variables

A linear equation in two variables can be expressed in the form (Ax + By = C), where (A), (B), and (C) are constants.
The equation (2x + 3y = 5) is an example of a linear equation that represents a straight line on a graph.

Solutions of Linear Equations

To find the solution of a linear equation, isolate the variable. For example, in the equation (2x + 5 = 15), subtract 5 from both sides, resulting in (2x = 10), leading to (x = 5).

Evaluating Linear Equations

For the equation (4x + 3y = 12), to find the value of (x) when (y = 0), substitute (y) with 0, resulting in (4x = 12); thus, (x = 3).

Matching Linear Equations with Slopes

The slope of a linear equation in the standard form (Ax + By = C) can be determined using the formula (m = -\frac{A}{B}).
Understanding the slope allows for determining the steepness and direction of the line represented by the linear equation.

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Description

Test your knowledge of linear equations in two variables with this quiz based on the Maharashtra state board curriculum. Answer questions that involve graphing, finding solutions, and analyzing slopes of equations. Perfect for reinforcing key concepts in math lesson 1.