Question

Write a pair of linear equations in two variables so that they represent parallel lines

Answer 1

Step-by-step explanation:

Linear equations in two variables are equations which can be expressed as ax + by + c = 0, where a, b and c are real numbers and both a, and b are not zero. The solution of such equations is a pair of values for x and y which makes both sides of the equation equal.

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Introduction

Let’s look at the solutions of some linear equations in two variables. Consider the equation 2x + 3y = 5. There are two variables in this equation, x and y.

Scenario 1: Let’s substitute x = 1 and y = 1 in the Left Hand Side (LHS) of the equation. Hence, 2(1) + 3(1) = 2 + 3 = 5 = RHS (Right Hand Side). Hence, we can conclude that x = 1 and y = 1 is a solution of the equation 2x + 3y = 5. Therefore, x = 1 and y = 1 is a solution of the equation 2x + 3y = 5.

Scenario 2: Let’s substitute x = 1 and y = 7 in the LHS of the equation. Hence, 2(1) + 3(7) = 2 + 21 = 23 ≠ RHS. Therefore, x = 1 and y = 7 is not a solution of the equation 2x + 3y = 5.

Answer 2

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Linear equations in two variables are equations which can be expressed as ax + by + c = 0, where a, b and c are real numbers and both a, and b are not zero. The solution of such equations is a pair of values for x and y which makes both sides of the equation equal.