Systems of Equations – Solving by Substitution Lesson 3-2 Part 1 Systems of Equations – Solving by Substitution

Solving Systems of Equations by Substitution Substitution – Replacing a variable with an equivalent term or expression. Ex. If x = 5 and x + y = 7, then 5 + y = 7 So to solve a system of linear equations, solve one equation for a variable, then substitute the expression into the other equation for that variable and solve. Once you know the value of that variable, replace into either of the starting equations to find the other variable’s value.

Example - Solving Systems of Equations by Substitution Given : y = x + 2 and y = -x + 4. Then x + 2 = -x + 4. Adding x and subtracting 2 from both sides gives you 2x = 2. Solve for x by dividing both sides by 2 yields that x = 1. Replace that into the first given equation yields y = 1 + 2 = 3 Solution is (1,3)

Example - Solving Systems of Equations by Substitution Given : 2x - 3y = 6 and x + y = -12. On Board.

Solving Systems of Equations by Substitution – Possible Solutions If you get a solution where 0 = 0 (true), then the lines overlap and there are an infinite number of solutions. Dependent Solution. If you get a solution like 3 = 5 (not true), then the lines are parallel, and there is not solution. Inconsistent.

Solving Systems of Equations by Substitution Advantages: Accurate Answer. Disadvantages: Algebra is a little cumbersome.

Assignment Page 128 1-6.