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Solving System of Linear Equations: (lesson 1 of 5)

The **substitution method** is most useful for systems of 2 equations in 2 unknowns.
The main idea here is that we solve one of the equations for one of the
unknowns, and then substitute the result into the other equation.

**Substitution method can be applied in four steps**

**Step 1:**

Solve one of the equations for either **x = ** or **y =** .

**Step 2:**

Substitute the solution from step 1 into the other equation.

**Step 3:**

Solve this new equation.

**Step 4:**

Solve for the second variable.

Example 1: Solve the following system by substitution

Solution:

**Step 1:** Solve one of the equations for either **x = ** or **y =** . We will solve
second equation for y.

**Step 2:** Substitute the solution from step 1 into the second equation.

**Step 3:** Solve this new equation.

**Step 4:** Solve for the second variable

**The solution is: (x, y) = (10, -5)**

Note: It does not matter which equation we choose first and which second. Just choose the most convenient one first!

Example 2: Solve by substitution

Solution:

**Step 1: Solve one of the equations for either x = or y =.**
Since the coefficient of y in equation 2 is -1, it is easiest to solve for y in equation 2.

**Step 2:** Substitute the solution from step 1 into the second equation.

**Step 3:** Solve this new equation ( for x ).

**Step 4:** Solve for the second variable

**The solution is: (x, y) = (1, 2)**

Level 1

Level 2