Solving Simultaneous Equations

SIMULTANEOUS EQUATIONS Algebra 3x 4y 7 (x 5y 12) 4x 9y 19 Adding the second equation to the first corresponds to adding the same quantity to both sides of the first equation. Thus, the resulting equation is still true. Similarly, two equations can be subtracted. 4x 3y 8 (2x 5y 11) 2x 8y 3 Subtracting the second equation from the first corresponds to subtracting the same quantity from both sides of the first equation. Thus, the resulting equation is still true. The basic approach used to solve a system of equations is to reduce the system by eliminating the unknowns one at a time until one equation with one unknown results. This equation is solved and its value used to determine the values of the other unknowns, again one at a time. There are three different techniques used to eliminate unknowns in systems of equations: addition or subtraction, substitution, and comparison. Solving Simultaneous Equations The simplest system of equations is one involving two linear equations with two unknowns. 5x + 6y = 12 3x + 5y = 3 The approach used to solve systems of two linear equations involving two unknowns is to combine the two equations in such a way that one of the unknowns is eliminated. The resulting equation can be solved for one unknown, and either of the original equations can then be used to solve for the other unknown. Systems of two equations involving two unknowns can be solved by addition or subtraction using five steps. Step 1. Multiply or divide one or both equations by some factor or factors that will make the coefficients of one unknown numerically equal in both equations. Step 2. Eliminate the unknown having equal coefficients by addition or subtraction. Step 3. Solve the resulting equation for the value of the one remaining unknown. MA-02 Page 32 Rev. 0