2 Substitution is an algebraic model that can be used to find the exact solution of a system of equation.What does substitution mean?Give examples of where we have used substitution in Math before this unit.
3 USING SUBSTITUTIONWhat is the solution of the system? Use substitution. Check your answer by using your graphing calculator. y = 3x and x + y = - 32Step 1: Because y = 3x, you can substitute 3x for y in x + y = - 32x + y = Write the second equation.x + 3x = -32 Substitute 3x for y4x = -32 Simplifyx = - 8 Divide each side by 4Step 2: Substitute – 8 for x in either equation and solve for y.y = 3x Write either equation.y = 3(- 8) = -24 Substitute – 8 for x and solve.The solution is (-8, - 24). Check by substituting (- 8, - 24) into each equation.
4 Let’s try one more together. What is the solution of the system? Use substitution.Check your answer by substituting your solution into each equation.Use your graphing calculator to check your answer.y = 2x + 7 and y = x - 1
5 With a partner, solve the following system using substitution With a partner, solve the following system using substitution. Show all work. Check your answer by graphing each equation on your graphing calculator.y = 3xx + y = 8
6 SOLVING FOR A VARIABLE AND USING SUBSTITUTION What is the solution of the system? Use substitution. 3y + 4x = 14 and -2x + y = -3Step 1: Solve one of the equations for one of the variables.-2x + y = Write the second equation.-2x + 2x + y = -3 Add 2x to each side.y = 2x – 3 Simplify.Step 2: Substitute 2x – 3 for y in the other equation and solve for x.3y + 4x = 14 Write the first equation.3(2x – 3) + 4x = 14 Substitute 2x – 3 for y. Use parentheses.6x– 9 + 4x = 14 Use the distributive property.10x = 23 Add 9 to each side and simplify.x = Divide each side by 10.
7 Step 3: Substitute 2.3 for x in either equation and solve for y. -2x + y = Write either equation.-2(2.3) + y = Substitute 2.3 for x.y = Simplify.y = Add 4.6 to each side.The solution is (2.3, 1.6).Use your graphing calculator to check your answer.
8 Let’s try one more together. What is the solution of the system? Use substitution.Use your graphing calculator to check your answer.6y + 5x = 8x + 3y = - 7Which variable did you solve for?Which equation did you use to solve for the variable?
9 With your partner, solve the system using substitution With your partner, solve the system using substitution. Check your answer by substituting and by using your graphing calculator.x + 3 = y3x + 4y = 7
10 Work to solve these systems. Show all your work. Check your answer. y = - x – 23x + y = 12y = 6x2x + 3y = - 20x = 2y + 7x = y + 4
11 Time to write……When is the substitution method a better method than graphing for solving a system of linear equations?For each system, tell which equation you would first use to solve for a variable in the first step of the substitution method. Explain your choice.a. -2x + y = -1 and 4x + 2y = 12b. x = 2y and 6x – y = 1Tell whether each statement is true or false. Explain.a. When solving a system using substitution, if you obtain an identity (an equation with infinitely many solutions), then the system has no solution.b. You cannot use substitution to solve a system that does not have a variable with a coefficient of 1 or – 1.