# Solving Systems of Equations Using Substitution

```Textbook Section 6-2
 Which
inequality does not have the same
2
solution as − 𝑦 &gt; 4?
3
A)
12 &lt; −2𝑦
B)
𝑦
2
C)
− 𝑦&gt;
D)
−3𝑦 &gt; 18
&lt; −12
3
4
9
2
 Students
can solve a system of equations
using substitution.
 Students can classify systems as consistent,
inconsistent, dependent, or independent
using algebraic methods.
 What
does the word substitute mean?
 Provide examples.
 In
sports, coaches often substitute one
player for another who plays the same
position.
 In school, when a teacher is absent, a
substitute teacher takes his/her place for the
day.
1)
2)
3)
4)
5)
Solve for either variable, if necessary.
Substitute the resulting expression into the
other equation.
Solve that equation to get the value of the
first variable.
Substitute that value into one of the
original equations and solve for the second
variable.
Write the values from steps 3 and 4 as an
Solve the following systems using substitution.
State the number of solutions (no solution, one
solution, or infinite solutions) and tell whether
the system is consistent, inconsistent,
dependent, or independent.
 Solve
the system using substitution.
𝑦 = 2𝑥
𝑦 =𝑥+5
One Solution
(5, 10)
Consistent
Independent
 Solve
the system using substitution.
2𝑥 + 𝑦 = 5
𝑦 =𝑥−4
One Solution
(3, -1)
Consistent
Independent
 Solve
the system using substitution.
𝑥 = 5𝑦 + 10
2𝑥 − 10𝑦 = 20
Infinite Solutions
Consistent
Dependent
Solve the system using substitution.
−5𝑦 − 𝑥 = −4
3𝑥 + 15𝑦 = −1
No Solution
Inconsistent
 When
solving the system, if the end result is
a false (for example, 2 = -5), the answer is
no solution.
 If
the end result is a statement that is always
true (for example, 3 = 3, or x = x), the
system has infinite solutions.
 If
you can solve for the variables, there is
one solution (for example, x = 3, y = 1).
```