Download 62 Solving Systems Using Substitution

6­2 Solving Systems Using Substitution substitution (noun) sub stuh TOO shun Related Words: substitute (verb or adjective) Definition: A substitution is something taking the place of something else. Example: A substitution of 4 for x and 8 for y in x + y gives 4 + 8 , or 12. Essential Understanding Systems of equations can be solved in more than one way. When a system has at least one equation that can be solved quickly for a variable, the system can be solved efficiently using substitution. You can solve linear systems by solving one of the equations for one of the variables. Then substitute the expression for the variable into the other equation. This is called the substitution method. Solve each system using substitution. Check your answer. A.) x + y = 8 y = 3x B.) x + 3 = y 3x + 4y = 7 C.) y =− 2x + 6 3y − x + 3 = 0 D.) y − 2x = 3 3x − 2y = 5 E.) 7x − 2y = 1 2y = x − 1 F.) Theater tickets Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost total of $228. Write and systems of equations to find how many children and how many adults were in the group. G.) Geometry The measure of one acute angle in a right triangle is four times the measure of the other acute angle. Write and solve a system of equations to find the measures of the acute angles. If you get an identity, like 2 = 2 , when you solve a system of equations, then the system has infinitely many solutions. If you get a false statement, like 8 = 2 , then the system has no solution. tell whether the system has one solution, infinitely many solutions, or no solution. H.) 6y =− 5x + 24 2.5x + 3y = 12 I.) 5 = 12 x + 3y 10 − x = 6y J.) 1.5x + 2y = 11 3x + 6y = 22