Algebra SIMULTANEOUS EQUATIONSSIMULTANEOUS EQUATIONSThis chapter covers solving for two unknowns using simultaneous equations.EO 1.4 Given simultaneous equations, SOLVE for theunknowns.Many practical problems that can be solved using algebraic equations involve more than oneunknown quantity. These problems require writing and solving several equations, each of whichcontains one or more of the unknown quantities. The equations that result in such problems arecalled simultaneous equations because all the equations must be solved simultaneously in orderto determine the value of any of the unknowns. The group of equations used to solve suchproblems is called a system of equations.The number of equations required to solve any problem usually equals the number of unknownquantities. Thus, if a problem involves only one unknown, it can be solved with a singleequation. If a problem involves two unknowns, two equations are required. The equation x +3 = 8 is an equation containing one unknown. It is true for only one value of x: x = 5. Theequation x + y = 8 is an equation containing two unknowns. It is true for an infinite set of xs andys. For example: x = 1, y = 7; x = 2, y = 6; x = 3, y = 5; and x = 4, y = 4 are just a few of thepossible solutions. For a system of two linear equations each containing the same two unknowns,there is a single pair of numbers, called the solution to the system of equations, that satisfies bothequations. The following is a system of two linear equations:2x + y = 9x - y = 3The solution to this system of equations is x = 4, y = 1 because these values of x and y satisfyboth equations. Other combinations may satisfy one or the other, but only x = 4, y = 1 satisfiesboth.Systems of equations are solved using the same four axioms used to solve a single algebraicequation. However, there are several important extensions of these axioms that apply to systemsof equations. These four axioms deal with adding, subtracting, multiplying, and dividing bothsides of an equation by the same quantity. The left-hand side and the right-hand side of anyequation are equal. They constitute the same quantity, but are expressed differently. Thus, theleft-hand and right-hand sides of one equation can be added to, subtracted from, or used tomultiply or divide the left-hand and right-hand sides of another equation, and the resultingequation will still be true. For example, two equations can be added.Rev. 0 Page 31 MA-02