Circles

Tips To Solve CAT Circles

- Fundamentals of this concept are useful in solving the questions of the other topics by assuming the unknown values as variables. Make sure to cover other inter-related concepts of CAT syllabus. All the inter-related concepts need to be covered to have a good foundation in concepts.

- Be careful of silly mistakes in this topic, as that is how students generally lose marks here. The number of equations needed to solve the given problem equals the number of variables. A linear equation is an equation which gives a straight line when plotted on a graph.

- If you are confused, enrolling in CAT online coaching will help you a long way.

- Linear equations can be of one variable or two variables, or three variables.

• Let a, b, c and d be constants, and x, y, and z are variables. A general form of a single variable linear equation is ax + b = 0.
• A general form of two-variable linear equation is ax + by = c.
• A general form of three-variable linear equation is ax + by + cz = d.

CAT Circles PDF

To help CAT aspirants in their preparation, we have made a comprehensive formula PDF containing all the important linear equations that are essential. This PDF includes all the necessary formulas, techniques, and examples required to solve linear equations efficiently. Click on the link below to download the Linear equations formula PDF.

1. Linear Equations Formulae: Solving Linear Equations

For equations of the form ax + by = c and mx + ny = p, find the LCM of b and n.

Multiply each equation with a constant to make the y term coefficient equal to the LCM. Then subtract equation 2 from equation 1.

2. Linear Equations Formulae: Straight Lines

Equations with 2 variables: Consider two equations ax + by = c and mx + ny = p. Each of these equations represents two lines on the x-y coordinate plane. The solution of these equations is the point of intersection.

If $\frac{a}{m}=\frac{b}{n}\ne \frac{c}{p}$: This means that both the equations have the same slope but different intercepts, and hence are parallel to each other. There is no point of intersection and no solution.

If $\frac{a}{m}\ne \frac{b}{n}$: They have different slopes and hence must intersect at some point, resulting in a unique solution.

If $\frac{a}{m}=\frac{b}{n}=\frac{c}{p}$: The two lines have the same slope and intercept. Hence, they are the same lines. As they have infinite points common between them, there are infinitely many solutions possible.