Can a linear equation have no zero?
A linear function can have none, one, or infinitely many zeros. If the function is a horizontal line ( slope = 0 ), it will have no zeros unless its equation is y=0 , in which case it will have infinitely many. If the line is non-horizontal, it will have one zero.
Is there a non-zero solution?
If the determinant is non-zero, then the slopes must be different and the lines must intersect in exactly one point. If this determinant is zero, then the system has either no nontrivial solutions or an infinite number of solutions.
Does a linear equation in two variables have infinite solutions?
A consistent pair of linear equations will always have unique or infinite solutions. Example 1) Here are two equations in two variables. Then the equation is a consistent and dependent equation which has infinitely many solutions.
How can you determine if an equation is a linear equation in two variables?
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
How many solutions can a linear equation in two variables have?
infinitely many solutions
Further, a linear equation in two variables has infinitely many solutions. The graph of every linear equation in two variables is a straight line and every point on the graph (straight line) represents a solution of the linear equation.
What equation has infinite solutions?
The equation 2x + 3 = x + x + 3 is an example of an equation that has an infinite number of solutions.
Are linear and simultaneous equations the same?
Two linear equations in two variables taken together are called simultaneous linear equations. The solution of system of simultaneous linear equation is the ordered pair (x, y) which satisfies both the linear equations.
What is the condition for no solution?
For no solution, Two lines have no solution, if these two lines are parallel to each other. The lines are parallel to each other means that the slopes of the lines are equal.
Why does linear equation in two variables have infinitely many solutions?
The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.
When we consider two linear equations in two variables such equations are called as?
A system of linear equations consists of two or more linear equations made up of two or more variables such that all equations in the system are considered simultaneously.
Which equation is a linear equation in two variables?
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
Can a linear equation have more than one solution?
Solutions of a Linear Equation of Two Variables A linear equation in one variable has a unique solution which means that there can’t be more than one solution for any given equation. But in the case of the linear equation having two variables, it can have infinite solutions because of the 2 variables that are present in the equation.
What happens if two linear equations have the same slope value?
If the two linear equations have equal slope value, then the equations will have no solutions. m1 = m2 This is because the lines are parallel to each other and do not intersect. System of Linear Equations in Two Variables
How do you find the standard form of a linear equation?
The standard form of a linear equation in one variable is represented as ax + b = 0 where, a ≠ 0 and x is the variable. The standard form of a linear equation in two variables is represented as. ax + by + c = 0, where, a ≠ 0, b ≠ 0 , x and y are the variables.