Presentation on theme: "The student will be able to:"— Presentation transcript:
1 The student will be able to: ObjectiveThe student will be able to:solve systems of equations using substitution.SOL: A.9Designed by Skip Tyler, Varina High School
2 Solving Systems of Equations You can solve a system of equations using different methods. The idea is to determine which method is easiest for that particular problem.These notes show how to solve the system algebraically using SUBSTITUTION.
3 Solving a system of equations by substitution Step 1: Solve an equation for one variable.Pick the variable that has a coefficient of 1Step 2: SubstitutePlug the equation solved in Step 1into the other equation.Step 3: Solve the equation.Isolate the variable.Step 4: Plug back in to find the other variable.Substitute your solution into the other equation.Step 5: Check your solution.Plug in your answer
4 1) Solve the system using substitution x + y = 5y = 3 + xStep 1: Solve an equation for one variable.The second equation isalready solved for y!Step 2: Substitutex + y = 5 x + (3 + x) = 52x + 3 = 52x = 2x = 1Step 3: Solve the equation.
5 1) Solve the system using substitution x + y = 5y = 3 + xx + y = 5(1) + y = 5y = 4Step 4: Plug back in to find the other variable.(1, 4)(1) + (4) = 5(4) = 3 + (1)Step 5: Check your solution.The solution is (1, 4). What do you think the answer would be if you graphed the two equations?
6 2) Solve the system using substitution 3y + x = 74x – 2y = 0It is easiest to solve thefirst equation for x.3y + x = 7-3y yx = -3y + 7Step 1: Solve an equation for one variable.Step 2: Substitute4x – 2y = 04(-3y + 7) – 2y = 0
7 2) Solve the system using substitution 3y + x = 74x – 2y = 0-12y + 28 – 2y = 0-14y + 28 = 0-14y = -28y = 2Step 3: Solve the equation.4x – 2y = 04x – 2(2) = 04x – 4 = 04x = 4x = 1Step 4: Plug back in to find the other variable.
8 2) Solve the system using substitution 3y + x = 74x – 2y = 0Step 5: Check your solution.(1, 2)3(2) + (1) = 74(1) – 2(2) = 0When is solving systems by substitution easier to do than graphing?When only one of the equations has a variable already isolated (like in example #1).
9 x + 4y = 4 3x + 2y = 22 -4y + 2 -4y + 4 -2x + 4 -2y+ 22 If you solved the first equation for x, what would be substituted into the bottom equation.x + 4y = 43x + 2y = 22-4y + 2-4y + 4-2x + 4-2y+ 22
10 3) Solve the system using substitution 2x + y = 44x + 2y = 8Step 1: Solve an equation for one variable.The first equation iseasiest to solved for y!y = -2x + 44x + 2y = 84x + 2(-2x + 4) = 8Step 2: Substitute4x – 4x + 8 = 88 = 8This is also a special case.Does 8 = 8? TRUE!Step 3: Solve the equation.When the result is TRUE, the answer is INFINITELY MANY SOLUTIONS.
11 What does it mean if the result is “TRUE”? The lines intersectThe lines are parallelThe lines are coincidingThe lines reciprocateI can spell my name