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Transcript
Objective: To solve a system of equations with substitution When you finish... turn in your graded warm-up and begin writing your notes. 5-2 Solving Systems by Substitution (p. 153) Another method used to solve systems is called the substitution method. USING THE SUBSTITUTION METHOD: 1) Solve one of the equations for a specific variable. (Pick the variable that does not have a coefficient.) 2) SUBSTITUTE the expression you solved in the other equation. 3) Solve the equation. 4) Substitute the value of the variable (from step 3) in EITHER equation to find the value of the other variable. 5) The solution is an ordered pair (x, y). Objective: To solve a system of equations with substitution Preview: (Do not Copy) Solve using substitution for y = 4x - 2 and 2x + 3y = -34. Substitute in 4x - 2 in for y in the equation 2x + 3y = -34 Substitute -2 for x and solve for y. 2x + 3y = -34 OR 2x + 3y = -34 2x + 3(4x-2) = -34 y = 4x - 2 2x + 12x - 6 = -34 y = 4(-2) - 2 2(-2) + 3y = -34 14x - 6 = -34 +6 +6 y = -8 - 2 -4 + 3y = -34 +4 +4 y = -10 3y = -30 3 3 14x = -28 14 14 y = -10 x = -2 solution = (-2, -10) Check: y = 4x - 2 2x + 3y = -34 -10 = 4(-2) - 2 2(-2) + 3(-10) = -34 -10 = -8 - 2 -4 + (-30) = -34 -10 = -10 -34 = -34 Objective: To solve a system of equations with substitution Ex 1: Solve by substitution y = 4x - 1 2x + 2y = 3 Objective: To solve a system of equations with substitution Ex 2: Solve the system by substitution y = 2x + 3 2x - 2y = 4 Objective: To solve a system of equations with substitution Example 3: Solve the system by substitution. -2x - 5y = -1 x + 3y = 4 (HINT: Solve for the variable that does not have a coefficient)