Download 5-2 Solving Systems by Substitution (p. 153)

Objective: To solve a system of equations with substitution
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5-2 Solving Systems by Substitution (p. 153)
Another method used to solve systems is called the substitution method.
USING THE SUBSTITUTION METHOD:
1) Solve one of the equations for a specific variable. (Pick the variable that
does not have a coefficient.)
2) SUBSTITUTE the expression you solved in the other equation.
3) Solve the equation.
4) Substitute the value of the variable (from step 3) in EITHER equation to find
the value of the other variable.
5) The solution is an ordered pair (x, y).
Objective: To solve a system of equations with substitution
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Solve using substitution for y = 4x - 2 and 2x + 3y = -34.
Substitute in 4x - 2 in for y in
the equation 2x + 3y = -34
Substitute -2 for
x and solve for y.
2x + 3y = -34
OR
2x + 3y = -34
2x + 3(4x-2) = -34
y = 4x - 2
2x + 12x - 6 = -34
y = 4(-2) - 2
2(-2) + 3y = -34
14x - 6 = -34
+6 +6
y = -8 - 2
-4 + 3y = -34
+4
+4
y = -10
3y = -30
3
3
14x = -28
14
14
y = -10
x = -2
solution = (-2, -10)
Check:
y = 4x - 2
2x + 3y = -34
-10 = 4(-2) - 2
2(-2) + 3(-10) = -34
-10 = -8 - 2
-4 + (-30) = -34
-10 = -10
-34 = -34
Objective: To solve a system of equations with substitution
Ex 1: Solve by substitution
y = 4x - 1
2x + 2y = 3
Objective: To solve a system of equations with substitution
Ex 2: Solve the system by substitution
y = 2x + 3
2x - 2y = 4
Objective: To solve a system of equations with substitution
Example 3: Solve the system by substitution.
-2x - 5y = -1
x + 3y = 4
(HINT: Solve for the variable
that does not have a coefficient)