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This algebra 2 math tutorial from NutshellMath offers targeted homework help in solving systems of equation algebraically. The instruction is focused on problems 15-22 on page 167 of the Algebra 2 with Trigonometry text from Prentice Hall. These homework problems present systems of equations with multiple variables. Solutions to such problems will ordered pairs representing the values of the variables for which all of the equations in the system are true.
In order to solve homework problems such as these, it is best to first clean up the equations so they are in the form Ax+By=C, where A and B are integer coefficients. To rewrite the equations in this form, it may be necessary to distribute to eliminate parentheses, and then use addition and subtraction to group variables and constants separately. Fractional and decimal coefficients can be eliminated by multiplying by the denominator for a fraction or powers of ten for decimals.
Once in the equations are in the standard form, linear combinations of the equations of the systems can be performed. The goal of a linear combination is to add or subtract a multiple of one of the equations to another equation in order to eliminate one of the variables from the sum. Doing so should yield a simpler equation that can be solved for a single variable as with a standard equation. When one of the variables has been found, it can then be substituted into the other equation to solve for the second variable. The values for the variables can be expressed as an ordered pair, which is the solution to the system of equations.
This tutorial presents methods for effectively simplifying and manipulating systems of equations. These techniques can be used to solve homework problems involving systems of equations, such as those targeted by this tutorial.
This algebra 2 math tutorial from NutshellMath offers targeted homework help in solving systems of equation algebraically. The instruction is focused on problems 15-22 on page 167 of the Algebra 2 with Trigonometry text from Prentice Hall. These homework problems present systems of equations with multiple variables. Solutions to such problems will ordered pairs representing the values of the variables for which all of the equations in the system are true.
In order to solve homework problems such as these, it is best to first clean up the equations so they are in the form Ax+By=C, where A and B are integer coefficients. To rewrite the equations in this form, it may be necessary to distribute to eliminate parentheses, and then use addition and subtraction to group variables and constants separately. Fractional and decimal coefficients can be eliminated by multiplying by the denominator for a fraction or powers of ten for decimals.
Once in the equations are in the standard form, linear combinations of the equations of the systems can be performed. The goal of a linear combination is to add or subtract a multiple of one of the equations to another equation in order to eliminate one of the variables from the sum. Doing so should yield a simpler equation that can be solved for a single variable as with a standard equation. When one of the variables has been found, it can then be substituted into the other equation to solve for the second variable. The values for the variables can be expressed as an ordered pair, which is the solution to the system of equations.
This tutorial presents methods for effectively simplifying and manipulating systems of equations. These techniques can be used to solve homework problems involving systems of equations, such as those targeted by this tutorial.