3.4C Solve Systems of Linear Equations in Three Variables (Using Substitution)
Goal · Solve systems of equations in three variables.
Example 1: Solve a system using Substitution
Solve the system. / 2x + y + z = 8 / Equation 1-x + 3y - 2z = 3 / Equation 2
y = x + z / Equation 3
1. Rewrite the system as a linear system in two variables by substituting x + z for y in Equations 1 and 2.
2x + y + z = 8 / Write Equation 1.
2x + (_____) + z = 8 / Substitute for y.
______= __ / New Equation 1
-x + 3y - 2z = 3 / Write Equation 2.
-x + 3(______) - 2z = 3 / Substitute for y.
______= ___ / New Equation 2
2. Solve the new linear system in two variables.
_______ / Add new Equation 1 and
_______ / _____ times new Equation 2.
x = ____ / Solve for x.
z = ___ / Substitute into new Equation 1 or new Equation 2 to find z
y = ___ / Substitute into an original equation to find y.
The solution is (______, ______, _____).
You Try: Solve the linear system.
1. z = - 2x + 2y + 7
4x - 4y + 2z = 17
3x + 2y - 6z = -2
Solve using the Substitution method.
Example 2: You Try:
Example 3: At a carry-out pizza restaurant, an order of 3 slices of pizza, 4 breadsticks, and 2 juices drinks cost $13.35. A second order of 5 slices of pizza, 2 breadsticks, and 3 juice drinks cost $19.50. If four breadsticks and a juice drink costs $.30 more than a slice of pizza, what is the cost of each item?