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What is the key to using the elimination method to find variable terms in the two equations that have equal or opposite coefficients?
Wiki User
∙ 14y ago
Eliminate the variables that have equal coefficients but opposite in sign.
x + 2y = 10
3x - 2y = 14
Or you can work to have one of the variables with equal coefficients but opposite in sign such as:
3x + 2y = 5
x + y = 2 multiply by -2 to both sides
3x + 2y = 5
-2x - 2y = -4
Wiki User
∙ 14y ago
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Four steps to the elimination method?
There are four steps in an algebraic elimination problem. These steps are: to find a variable with equal or opposite coefficients, if equal then subtract the equations but if opposite then add, solve one variable equation left, and then substitute known variable into other equation and solve. hi
What is a method for solving a system of linear equations in which you multiply one or both equations by a number to get rid of a variable term?
It is called solving by elimination.
How do you find the solution to a system of equation?
There are several methods. 1. graphing, then find the intersection. 2. Substitution (take one equation and solve for one variable, substitute that into the 2nd equation) 3. Elimination. Arrange both equations in standard form, arrange so that the coefficients on one of the variables are the same and subtract the 2 equations. 4. Cramer's rule, use matrices to solve.
How does writing equivalent equations help you solve a system of equations?
You can write an equivalent equation from a selected equation in the system of equations to isolate a variable. You can then take that variable and substitute it into the other equations. Then you will have a system of equations with one less equation and one less variable and it will be simpler to solve.
Why is substitution the best method in solving systems of equations?
It is not always the best method, sometimes elimination is the way you should solve systems. It is best to use substitution when you havea variable isolated on one side
True or false The key to using the elimination method is to find variable terms in the two equations that have equal or opposite coefficients?
True
Four steps to the elimination method?
There are four steps in an algebraic elimination problem. These steps are: to find a variable with equal or opposite coefficients, if equal then subtract the equations but if opposite then add, solve one variable equation left, and then substitute known variable into other equation and solve. hi
What is a mathematical statement that has two unequal quantities?
The key to using the elimination method is to find variable terms in two equations that have unequal coefficients
To solve a three variable system of equations you can use a combination of the elimination and substitution methods?
True. To solve a three variable system of equations you can use a combination of the elimination and substitution methods.
How do you determine the values of x and y in a linear equation in two variables?
There are 4 ways to do it. You can graph, use substitution, use elimination, or use matrices. Graphing: Graph the two equations and the coordinates where they intersect are the answer. Substitution: Solve one of the equations for one of the variables and substitute that in the other equation. Then you'll find the value of that variable and you can substitute that and get the other variable. Elimination: Make the coefficients of one of the variables opposites of each other and then add both equations. The opposites will cancel and you have the other variable. Then when you find that variable, find the other one by substituting the number for that variable in one of the equations. Matrices: Make sure both equations are in standard form (Ax+By=C). Then make a 2x2 matrix that has the coefficients of x in the left column and the coefficients of y in the right column and each equation gets its own row. Then make a 2x1 matrix with the C values. Put the C value of the equation you put at the top at the top and the other one at the bottom. Then multiply the inverse of the 2x2 matrix by the 2x1 matrix and you'll get a 2x1 matrix with x at the top and y at the bottom.
What is a method for solving a system of linear equations in which you multiply one or both equations by a number to get rid of a variable term?
It is called solving by elimination.
When you have two linear equations how do you know when they are all real numbers?
The answer depends on what are meant to be real numbers! If all the coefficients are real and the matrix of coefficients is non-singular, then the value of each variable is real.
How do you solve a system of equations by graphing?
Write each equations in popular form. ... Make the coefficients of one variable opposites. ... Add the equations ensuing from Step two to remove one variable. Solve for the last variable. Substitute the answer from Step four into one of the unique equations.
How do you use different techniques to solve linear equations?
There are several techniques to solve linear equations. One common technique is the elimination method, where you eliminate one variable by adding or subtracting equations. Another technique is substitution, where you solve one equation for a variable and substitute it into the other equation. You can also use matrices and row operations to solve linear equations.
How do you find the solution to a system of equation?
There are several methods. 1. graphing, then find the intersection. 2. Substitution (take one equation and solve for one variable, substitute that into the 2nd equation) 3. Elimination. Arrange both equations in standard form, arrange so that the coefficients on one of the variables are the same and subtract the 2 equations. 4. Cramer's rule, use matrices to solve.
Is The elimination method is useful when you can eliminate one of the variable terms from an equation by adding or subtracting another equation?
Yes, for solving simultaneous equations.
How do you decide whether to use elimination or subsitution to solve a three-variable system?
There is no simple answer. Sometimes, the nature of one of the equations lends itself to the substitution method but at other times, elimination is better. If they are non-linear equations, and there is an easy substitution then that is the best approach. With linear equations, using the inverse matrix is the fastest method.
