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How do you use different techniques to solve linear equations?
1. Elimination: Select two equations and a variable to eliminate. Multiply each equation by the coefficient if that variable in the other equation. If the signs of the coefficient for that variable in the resulting equations are the same then subtract one new equation from the other. If they have opposite signs then add them. You will now have an equation without that variable. Repeat will other pairs and you will end up with one fewer equation and one fewer variable. Repeat this process: after each round you will have one fewer equation and one fewer variable. Keep going until you are left with one equation in one variable. Solve that. Then work backwards solving for the other variables.2. Substitution: Select a equation and a variable. Make that variable the subject of the equation. The right hand side of this equation is an expression for that variable. Substitute this expression for the variable is each of the other equations. Again, one fewer equation in one fewer variable. Continue until you are left with one equation in one variable. Solve that. Then work backwards solving for the other variables.3. Matrix inversion: If A is the nxn matrix of coefficients, X is the nx1 [column] matrix of variables and B is the nx1 matrix of the equation constants, then X = A^-1*B where A^-1 is the inverse of matrix A.
When should you use the addition property of equality to eliminate one variable in a system of equation?
When the coefficient of that variable, in which you want to eliminate, is negative.
What reduces a equation that has two variables to an equation that has one variable?
combining like terms or subtracting from both sides of the equation.
What reduces an equation that has two variables to an equation that has one variable. It is then possible to find the solution for this variable.?
substitution
Can you solve a variable with an equation?
When an equation has a variable in it (only one), then there are only certainvalues the variable can have that will make the equation a true statement."Solving" the equation means finding those values for the variable.
The elimination method is useful when you can eliminate one of the variable terms from an equation by adding or subtracting another equation?
True
What is 2y-2x-8 3y-18-3x using elimination method?
To solve this system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the two equations. By looking at the equations given (2y-2x-8 = 0 and 3y-18-3x = 0), we can choose to eliminate either the x or y variable. Let's choose to eliminate the x variable: Multiply the first equation by 3 and the second equation by 2 to make the coefficients of x the same: 6y - 6x - 24 = 0 6y - 36 - 6x = 0 Now we can subtract the second equation from the first equation to eliminate x: (6y - 6x - 24) - (6y - 36 - 6x) = 0 Simplify to get -12 = 0, which is a false statement. Therefore, the system of equations is inconsistent and has no solution.
How do you find system of linear equation in two variable?
By elimination and substitution
When subtracting an algebraic equation which comes first a variable or the constant?
It does not matter.
How do you use different techniques to solve linear equations?
1. Elimination: Select two equations and a variable to eliminate. Multiply each equation by the coefficient if that variable in the other equation. If the signs of the coefficient for that variable in the resulting equations are the same then subtract one new equation from the other. If they have opposite signs then add them. You will now have an equation without that variable. Repeat will other pairs and you will end up with one fewer equation and one fewer variable. Repeat this process: after each round you will have one fewer equation and one fewer variable. Keep going until you are left with one equation in one variable. Solve that. Then work backwards solving for the other variables.2. Substitution: Select a equation and a variable. Make that variable the subject of the equation. The right hand side of this equation is an expression for that variable. Substitute this expression for the variable is each of the other equations. Again, one fewer equation in one fewer variable. Continue until you are left with one equation in one variable. Solve that. Then work backwards solving for the other variables.3. Matrix inversion: If A is the nxn matrix of coefficients, X is the nx1 [column] matrix of variables and B is the nx1 matrix of the equation constants, then X = A^-1*B where A^-1 is the inverse of matrix A.
When should you use the addition property of equality to eliminate one variable in a system of equation?
When the coefficient of that variable, in which you want to eliminate, is negative.
What reduces a equation that has two variables to an equation that has one variable?
combining like terms or subtracting from both sides of the equation.
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 y2x-5 eliminated?
7
What is an equation with one or two variables?
When you solve a one-variable equation, your goal is to isolate the variable.To isolate the variable means to make it be alone on one side of the equals sign.In the equation shown here, you can isolate the variable by subtracting 9 from both sides of the equation and simplifying
What reduces an equation that has two variables to an equation that has one variable. It is then possible to find the solution for this variable.?
substitution
Can you solve a variable with an equation?
When an equation has a variable in it (only one), then there are only certainvalues the variable can have that will make the equation a true statement."Solving" the equation means finding those values for the variable.
