Presentation on theme: "Solving Systems of Equations By Substitution – Easier"— Presentation transcript:
1 Solving Systems of Equations By Substitution – Easier Dr. Fowler CCMSolving Systems of Equations By Substitution – Easier
2 Solving a system of equations by substitution Step 1: Solve an equation for one variable.Pick the easier equation. The goalis to get y= ; x= ; a= ; etc.Step 2: SubstitutePut the equation solved in Step 1into the other equation.Step 3: Solve the equation.Get the variable by itself.Step 4: Plug back in to find the other variable.Substitute the value of the variableinto the equation.Step 5: Check your solution.Substitute your ordered pair intoBOTH equations.
3 EXAMPLE 1 Solve by substitution: The second is solved for X. Substitute this into OTHER equation for X:Substitute found y into other equation:The solution set found by the substitution method will be the same as the solution found by graphing. The solution set is the same; only the method is different. ALWAYS put answer in Alphabetical order. (x,y)
4 2) 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 2) 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 3) Solve the system using substitution x = 3 – yx + y = 7Step 1: Solve an equation for one variable.The first equation isalready solved for x!Step 2: Substitutex + y = 7(3 – y) + y = 73 = 7The variables were eliminated!!This is a special case.Does 3 = 7? FALSE!Step 3: Solve the equation.When the result is FALSE, the answer is NO SOLUTIONS.
7 4) 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.
8 Example 5) Solve the following system of equations using the substitution method. y = 3x – 4 and 6x – 2y = 4The first equation is already solved for y. Substitute this into second equation.6x – 2y = 46x – 2(3x – 4) = 4 (substitute)6x – 6x + 8 = 4 (use distributive property)8 = (simplify the left side) Does 8=4? FALSE.Examples like this – the answer is NO SOLUTION Ø. If you graphed them, they would be PARALLEL LINES.
9 EXAMPLE 6 Solve the system by the substitution method. The second is solved for X. Substitute this into OTHER equation for X:Substitute found y into other equation:
10 Example #7:y = 4x3x + y = -21Step 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
11 y = 4x3x + y = -21Step 4: We found x = -3. Now, substitute this into either original equation to find y:y = 4x (easiest)y = 4(-3)y = -12Solution to the system is (-3, -12).