Transcript Chapter 7.2 Notes: Solve Linear Systems by Substitution

Chapter 7.2 Notes: Solve Linear
Systems by Substitution
Goal: You will solve systems of linear
equations by using substitution.
• Solving a Linear System Using the Substitution
Method:
Step 1: Solve one of the equations for one of its
variables. When possible, solve for a
variable that has a coefficient of 1 or -1.
Step 2: Substitute the expression from Step 1 into
the other equation and solve for the other
variable.
Step 3: Substitute the value from Step 2 into the
revised equation from Step 1 and solve.
• Solve each system of linear equations by
substitution. Then check your solution.
Ex.1: y  3x  2
Ex.2: x  2 y  6
4x  6 y  4
x  2 y  11
Ex.3: y  2 x  3
x  3y  5
Ex.5: y  2 x  5
3 x  y  10
Ex.4: 5 x  y  12
3x  5 y  4
Ex.6: 3 x  y  7
2 x  4 y  0
Ex.7: x  y  3
x  2 y  6
Ex.8: The sum of two numbers is 35. The first
number is four times the second number. Find the
numbers.
Ex.9: During a football game, students sell drinks
and popcorn. They charge $2.50 for a bag of
popcorn and $2 for a drink. The students collect
$336 in sales. They sell twice as many bags of
popcorn as drinks. How many bags of popcorn do
they sell?
Ex.10: You have twice as many apples as oranges,
and you have 12 apples and oranges altogether.
How many apples and oranges do you have?
Ex.11: A group of friends take a day-long tubing trip.
The rental shop charges $15 to rent a tube for a
person and $7.50 to rent a “cooler” tube, which is
used to carry food in a cooler. The friends spend
$360 to rent a total of 26 tubes. How many of
each type of tubes do they rent?