3.2 Solving Linear Systems by Substitution

Objective: solve a system of linear equations in two variables by

substitution

What is the substitution method?When would we use it?

Solving a Linear System by Substitution

1. Solve one equation for one of its variables.2. Substitute the expression from Step 1 into

the other equation and solve for the other variable.

3. Substitute the value from Step 2 into the revised equation from Step 1 and solve.

4. Check the solution in each of the original equations.

Use substitution

Equation 1: y = 2xEquation 2: 4x – y = 6

Use substitution

Equation 1: 3x + 2y = 7Equation 2: x – 2y = -3

Practice

3x + 2y = 1-2x + y = -4

Practice

1. 2x + y = 3 & 3x + y = 0

2. 2x + 3y = 4 & x + 2y = 1

3. 3x – y = 5 & 4x + 2y = 10

On one day, the Rock and Roll Hall of Fame in Cleveland, Ohio, admitted 4400 adults and students and collected $57,200 in ticket sales. The price of admission is $14 for an adult and $10 for a student. How many adults and how many students were admitted to the museum that day?

On one day, the American Museum of Natural History in New York City, admitted 541 adults and children and collected $9020 in ticket sales. The price of admission is $40 for an adult and $11 for a child. Find how many adults and children were admitted to the museum on that day.

Your friend bought a total of 8 pounds of sliced turkey and sliced ham for a party. The sliced turkey costs $3/lb and the sliced ham costs $4/lb. The total cost was $28.50. How much of each type of meat did your friend buy?