Solving Linear Systems Using Substitution There are two methods of solving a system of equations algebraically: Elimination Substitution - usually used.

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Presentation transcript:

Solving Linear Systems Using Substitution There are two methods of solving a system of equations algebraically: Elimination Substitution - usually used when one variable has a coefficient of 1 or -1

Substitution To solve a system of equations by substitution… 1.Solve one equation for one of the variables. (Solve for easiest variable to solve for.) 2.Substitute the value of the variable into the other equation. 3.Simplify and solve the equation. 4.Substitute back into any equation to find the value of the other variable.

Substitution Solve the system: x - 2y = -5 y = x one variable is already solved for (y) Substitute (x + 2) for y in the first equation to solve for x. x - 2y = -5Original Equation x - 2(x + 2) = -5 Substitute x - 2x – 4 = -5Multiply -x - 4 = -5Combine like terms -x = -1Add 4 to both sides x = 1Multiply both sides by -1

Substitution Solve the system: x - 2y = -5 y = x + 2 y = x + 2Equation x = 1 y = 1 + 2Substitute y = 3Solve Solution: (1, 3)

Substitution ● Let’s check the solution. The answer (1, 3) must check in both equations. x - 2y = -5 y = x (3) = -53 = = -5  3 = 3 

Guided Practice Solve the system: 2p + 3q = 2 p - 3q = -17 Check your answer.

Writing and Using a Linear System An AMC movie theater has 345 customers in one day and makes $3555 in ticket sales. Adult tickets are $11 and student tickets are $9. How many adults and students were there? Solution Verbal Model: #Adults + #Students = Total Tickets (#Adults)($Adult) + (#Students)($Student) = Total Cost

Writing and Using a Linear System Solution x = Adults y = Students x + y = 345Substitute 11x + 9y = 3555

Writing and Using a Linear System Solution x + y = x + 9y = 3555 x + y = 345 y = xIsolate Variable 11x + 9(345 - x) = x x = 3555Distributive Property 2x = 3555Combine Like Terms 2x = 450Subtract x = 225Divide

Writing and Using a Linear System Solution x + y = 345 x = y = 345 y = 120 Answer There were 225 adults and 120 students. (225, 120) 11x + 9y = 3555 x + y = 345 *You can also check by graphing.

Independent Practice Solve the linear systems by substitution: 1.x = 4 2x - 3y = x + y = 7 4x + 2y = 16