Adapted from Walch Education Proving Equivalencies.

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Presentation transcript:

Adapted from Walch Education Proving Equivalencies

›Two equations that are solved together are called systems of equations. ›The solution to a system of equations is the point or points that make both equations true. ›Systems of equations can have one solution, no solutions, or an infinite number of solutions. ›Solutions to systems are written as an ordered pair, (x, y). Systems of Equations

›Solve one of the equations for one of the variables in terms of the other variable. ›Substitute, or replace the resulting expression into the other equation. ›Solve the equation for the second variable. ›Substitute the found value into either of the original equations to find the value of the other variable. Solving Systems of Equations by Substitution

›Multiply each term of the equation by the same number. It may be necessary to multiply the second equation by a different number in order to have one set of variables that are opposites or the same. ›Add or subtract the two equations to eliminate one of the variables. ›Solve the equation for the second variable. ›Substitute the found value into either of the original equations to find the value of the other variable. Solving Systems of Equations by Elimination Using Multiplication

›Solve the following system by elimination. Practice # 1

› Add the two equations if the coefficients of one of the variables are opposites of each other. ›3y and –3y are opposites: ›Simplify : 3x = 0 › Solve the equation for the second variable. ›x = 0 ›We are half way there!!!

› Substitute the found value, x = 0, into either of the original equations to find the value of the other variable. 2x – 3y = –11First equation of the system 2(0) – 3y = –11Substitute 0 for x. – 3y = –11Simplify. Divide both sides by –3. If graphed, the lines would cross at

Don’t worry, we will practice elimination method and substitution method in class!

~ Dr. Dambreville Thanks for Watching!!!!