Class 10th English Medium - Class 12 UP Board Maths

Pair of Linear Equations in Two Variables

Meaning and Structure of Linear Equations A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. When plotted on a graph, a linear equation in two...

If a pair of linear equations is given by $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ and $\frac{a_1}{a_2}=\frac{b_1}{b_2}\≠\frac{c_1}{c_2}$ . In this case, the pair of linear equations is consistent.

False

Which of the following statements is false?

General form of linear equation in two variables is <em>ax</em> + <em>c</em> = 0

Statement I: Solution of a linear equation ax + by + c = 0 is the values of x &amp; y which satisfy the equation.

Statement II: a &ne; 0, b &ne; 0, c = 0, the equation will be of the form ax + by = 0. This line passes through origin.

Both statements are true

The solution of the pair of linear equations $\frac{2x}{3}-\frac{y}{2}+\frac{1}{6}=0$ and $\frac{x}{2}+\frac{2y}{3}=3$ is:

x = 2, y = 3

What is a linear equation in two variables?

An equation of the form $ax + by + c = 0$, where $a$, $b$, and $c$ are real numbers and $a, b \neq 0$. Each solution $(x, y)$ represents a point on a straight line in the Cartesian plane.

Define algebraic expression.

A mathematical phrase containing constants, variables, and operators but no equality or inequality sign. For example, $3x + 2y$ is an algebraic expression.