How Do You Solve Linear Systems Algebraically?
You have several options when you need to solve systems of linear equations. One of the most accurate methods is to solve the problem algebraically. This method is accurate because it eliminates the risk of making a graphing error. In fact, using algebra to solve systems of linear equations eliminates the need for graph paper altogether. This is the best method to use when working with systems of equations that include many fractions or appear to have fractional answers. Start by solving one of the equations for either x or y. Choose the one that is the simplest to solve. In 2x – 3y = -2, 4x + y = 24, it is easiest to solve the second equation for y by subtracting 4x from both sides, giving you y = -4x + 24. Substitute this value into the first equation for y. This gives you 2x – 3 (-4x + 24) = -2. Notice how the y variable is now eliminated. Simplify the resulting equation. This gives you 2x + 12x – 72 = -2. This simplifies to 14x – 72 = -2. Solve this equation for x. Start by adding
