Presentation on theme: "Systems of Equations Standards: MCC9-12.A.REI.5-12"— Presentation transcript:
1 Systems of Equations Standards: MCC9-12.A.REI.5-12 Objectives: To solve systems of linear equations by substitution, elimination and graphing.
2 Solving Systems of Equations using Substitution Steps:1. Solve one equation for one variable (y= ; x= ; a=)2. Substitute the expression from step one into the other equation.3. Simplify and solve the equation.4. Substitute back into either original equation to findthe value of the other variable.5. Check the solution in both equations of the system.
3 y = 4x3x + y = -21ExampleStep 1: Solve one equation for one variable.y = 4x (This equation is already solved for y.)Step 2: Substitute the expression from step one into the other equation.3x + y = -213x + 4x = -21Step 3: Simplify and solve the equation.7x = -21x = -3
4 y = 4x 3x + y = -21 Step 4: Substitute back into either original equation to find the value of the othervariable.3x + y = -213(-3) + y = -21-9 + y = -21y = -12Solution to the system is (-3, -12).
5 Solving Systems of Equations using Elimination Steps:1. Place both equations in Standard Form, Ax + By = C.2. Determine which variable to eliminate with Addition or Subtraction.3. Solve for the variable left.4. Go back and use the found variable in step 3 to find second variable.5. Check the solution in both equations of the system.
6 5x + 3y = 115x = 2y + 1EXAMPLESTEP1: Write both equations in Ax + By = Cform x + 3y =15x - 2y =1STEP 2: Use subtraction to eliminate 5x x + 3y = x + 3y = 11-(5x - 2y =1) x + 2y = -1Note: the (-) is distributed.STEP 3: Solve for the variable.5x + 3y =11-5x + 2y = -15y = y = 2
7 The solution to the system is (1,2). 5x + 3y = 115x = 2y + 1STEP 4: Solve for the other variable by substitutinginto either equation.5x + 3y =115x + 3(2) =115x + 6 =115x = 5x = 1The solution to the system is (1,2).
8 Solving Systems of Equations By Graphing Steps:1. Graph both lines2. The point of intersection is the solution3. If the lines do not intersect (or are parallel), there are NO solutions4. If the lines are actually the same, there are INFINITE solutions.5. You do NOT shade equations, only inequalities.
9 Solving Systems of Equations By Graphing Solve the following system of equations:y = 2x + 1y = ½x + 3