You can then substitute Z=3 into equation (4) It would be best if you then solved equation (1) and (4) since they are 2×2 system linear equation by subtracting. Please, multiply equation (2) by a suitable constant,say ( -3) to get: Then, select equation (2) and (3) to eliminate Y. In this case, select Y since it is missing in equation (1). Next, choose a suitable variable to eliminate. Example 2įirst, write all the equations in standard form. Therefore the solution is X=1, Y =-1 and Z = 2. Use the answers obtained to substitute into any equation involving the remaining variable. Now substitute Z=2 in any of the created 2×2 system, that is (4) or (5). To eliminate X, multiply equation (1) with (-2) or any other suitable constant. You should then select a different set of two equations, in this case, equations (1) and (3) to eliminate the same variable. You should then select two equations with which to eliminate X. In this case, you realize that the system is already in standard form therefore, choose the variable to eliminate, for instance, X. Task: Solve the following system of equations using the elimination method. Check to prove the solution with all the three original equations. Substitute the answers in step five into any equation that has the remaining variable.ħ. Solve the two equations in steps three and four for the two variables they contain.Ħ. Select a different set of the two equations and eliminate the same selected variable.ĥ. Choose any two of the three equations and eliminate the selected variable.Ĥ. Select a suitable variable to eliminate.ģ. Put all the equations in standard form, avoiding decimals and fractions.Ģ. This complexity is a result of the additional variable.Īlthough there are several methods for solving this type of equation, the elimination method remains the most straightforward.įollow the procedure below to use the elimination method in solving three variable linear equations:ġ. 6X-8Y+Z=-22 Using the Elimination Method to Solve a Three Variable Linear EquationĪ three-variable linear equation is a bit more difficult to solve compared to equations with two variables. Examples Relating to Three Variable Linear Equations A system here refers to when you have two or more equations working together. There are several systems of linear equations involving the same set of variables.
The variables, which on most occasions are real numbers, are considered the parameters of the equation. A Linear equation usually results in a straight line when plotted graphically. Will review the submission and either publish your submission or provide feedback.An equation between two variables is known as a Linear equation. You can help us out by revising, improving and updatingĪfter you claim an answer you’ll have 24 hours to send in a draft. Use the first equation:Ĭombine like terms on the left side of the equation: Substitute the values for $y$ and $z$ we just found into one of the original equations to solve for $x$. Subtract $1$ from each side of the equation:ĭivide both sides of the equation by $3$ to solve for $z$: Substitute this value for $y$ into the sixth equation to solve for $z$: Multiply equation $4$ by $-1$:Ĭombine equations $5$ and $6$ to eliminate the $z$ variable:ĭivide both sides by $4$ to solve for $y$: Modify equation $4$ such that one variable is the same in equations $4$ and $5$ but differs in sign. Substitute this expression for $x$ into both equations $1$ and $2$: Subtract $2z$ from both sides of the equation:
The first step is to isolate the $x$ variable in equation $3$.
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