How do you solve linear equations ?

Question

please help

Answer 1

A linear equation is an equation of straight line on a graph.

General form of the linear equation is ax + by + c = 0

Where (a and b both cannot be zero).

A system of linear equations would be more than one line.

To solve such a system of linear equations means to find the point (x, y) a which these two lines intersect.

If the two lines do indeed intesect, then you can find the point of intersection.

Algebracally or by graphing the two lines and inspecting the graph to find the point of intrsection.

This is called a " consistent system"

If the two lines are do not intersect, then there are two possibilities.

1) they are parallel, in which case, there is no point of intersection and thus, no solution to this system of equations.

This is called "inconsistent system"

2) The two lines are collinear(one lies on top of the other).

In which case, there is an infinite number of solutions because any point that lies on one of the lines will also lie on the other line.

This is a consistent system and the equations are " depenent equations"

To solve linear equations algebraically

The elimination method

To use the elimination method, you use the to multiply both equations by the number necessary so that when adding or subtracting the equations, one of the variables is eliminated.

Then you would substitute that value into either original equation to find the value of the other variable.

The substitution method

To use the substitution method, you solve one of the equations for either variable, and then substitute that algebra expression in for the same variable in the other equation.

This will allow you to solve for one variable.

Then you would substitute that value into either original equation to find the value of the other variable.

Cross - multiplication method

Let’s consider the general form of a pair of linear equations.
, and .

To solve this pair of equations for  and  using cross-multiplication,

we’ll arrange the variables  and  and their coefficients , ,  and , and the constants  and  as shown below


.