Solving Systems of Equations
A system of equations consists of more than one linear
equation each containing the same two variables. The solution of a
system is the ordered pair or pairs which make both of the linear equations
true at the same time. To determine if an ordered pair is a solution
to a system, the ordered pair must “work” in all equations in the system.
For example, if (3, 4) satisfies both 2x + y = 10 and 3x + 2y = 17, then (3,
4) is said to be the solution to that system of equations. Since 2(3)
+ 4 = 10 is true and 3(3) + 2(4) = 17 is true, then (3, 4) is the solution
to the system. Try (4, 3) in the system, x + 2y =10 and 3x + 5y = 3 …
(4) + 2(3) = 10 is true, 3(4) + 5(3) = 3 is false; therefore, (4, 3) is not
a solution to the system since
There are three possible solutions to a system of
Graphing a system of equations allows a “picture” of the solution. If two linear equations are graphed on the same axis then their solution is the point of intersection. You may review graphing lines.
If you graph two lines onto one coordinate axis and note the intersection, if any, then you will have solved that system. Graphing systems of equations to determine a solution is a very inaccurate method, especially when there are fractional answers. The remaining two methods Substitution and Elimination are algebraic and very accurate.
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