Table of Contents

## How do you find a solution?

To solve for , you must first combine the ‘s on the right side of the equation. This will give you . Then, subtract and from both sides of the equation to get . Finally, divide both sides by to get the solution .

## How do you tell if there are infinitely many solutions?

The equation simplifies to the point that it no longer contains a variable, but expresses a true equation, e.g. 0=0 . For example: 2x+2=2(x+1) simplifies in this way. The equation has an identifiable solution and is periodic in nature. For example: tan2x+tanx−5=0 has infinitely many solutions since tanx has period π .

## Does the initial value problem have a unique solution?

That is, the theorem guarantees that the given initial value problem will always have (existence of) exactly one (uniqueness) solution, on any interval containing t0 as long as both p(t) and g(t) are continuous on the same interval.

## How do you know if a solution is unique?

Condition for Unique Solution to Linear Equations A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point. i.e., if the two lines are neither parallel nor coincident.

## What is the unique solution?

By the term unique solution, one mean to say that only one specific solution set exists for a given equation. So, if we have two equations, then unique solution will mean that there is one and only point at which the two equations intersect.

## What is the condition of no solution?

If there are infinitely many solutions of the given pair of linear equations, the equations are called dependent (consistent). If the lines are parallel, there is no solution for the pair of linear equations. If there is no solution of the given pair of linear equations, the equations are called inconsistent.

## How do you find no solution?

To find the missing number, compare both sides of the equation. If the variable terms are the same and the constant terms are different, then the equation has no solutions.

## How many solutions do 2 parallel lines have?

Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.

## What is symbol for no solution?

symbol Ø

## How do you write a solution?

When you write your solution you should:

- Give each important definition or equation its own line.
- Don’t bury too much algebra in a paragraph.
- Label equations or formulas or lemmas or cases you will use later very clearly.
- Remember that there’s always more paper.

## How do you tell if an equation has no solution?

The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur. Use distributive property on the right side first.

## How do you tell the number of solutions an equation has?

If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.

## How do you know if an equation has 2 solutions?

The discriminant is the part under the square root in the quadratic formula, b²-4ac. If it is more than 0, the equation has two real solutions. If it’s less than 0, there are no solutions. If it’s equal to 0, there is one solution.