how many way to solve system of linear equation
Answers
Step-by-step explanation:
three ways
There are three ways to solve systems of linear equations in two variables: graphing. substitution method. elimination method.
Answer:
The three methods most commonly used to solve systems of equation are substitution, elimination and augmented matrices. Substitution and elimination are simple methods that can effectively solve most systems of two equations in a few straightforward steps. The method of augmented matrices requires more steps, but its application extends to a greater variety of systems.
Substitution
Substitution is a method of solving systems of equations by removing all but one of the variables in one of the equations and then solving that equation. This is achieved by isolating the other variable in an equation and then substituting values for these variables in other another equation. For example, to solve the system of equations x + y = 4, 2x - 3y = 3, isolate the variable x in the first equation to get x = 4 - y, then substitute this value of y into the second equation to get 2(4 - y) - 3y = 3. This equation simplifies to -5y = -5, or y = 1. Plug this value into the second equation to find the value of x: x + 1 = 4 or x = 3.
Elimination
Elimination is another way to solve systems of equations by rewriting one of the equations in terms of only one variable. The elimination method achieves this by adding or subtracting equations from each other in order to cancel out one of the variables. For example, adding the equations x + 2y = 3 and 2x - 2y = 3 yields a new equation, 3x = 6 (note that the y terms cancelled out). The system is then solved using the same methods as for substitution. If it is impossible to cancel out the variables in the equations, it will be necessary to multiply the entire equation by a factor to make the coefficients match up.