# How to Solve Linear Equations with 2 Variables – Tutorial and Practice

- Posted by Brian Stocker MA
- Date November 27, 2014
- Comments 0 comment

### Linear Equations with 2 Variables

A system of a linear equations have two or more equations and two variables. In a system of linear equations, each equation is a straight line and the solution will be the point where the two lines intersect.

### How to Solve Linear Equations with 2 Variables – Quick Review Tutorial

If we have 2 or more linear equations with 2 or more variables, then we have a system of linear equations. Here, we will solve systems with 2 variables, given in 2 linear equations. Idea here is to express one variable using the other variable in one equation, and use it in the second equation, where we would get a linear equation with one variable. Let’s the how it works in one simple example:

x – y = 3

__2x + y = 9__

y = x – 3

2x + x – 3 = 9

3x = 9 + 3

From the first equation, we express y using x.

In the second equation, we write x – 3 instead of y. And there we get a linear equation with one variable x.

3x = 12

x = 12/3

__x = 4__

Now that we found x, we can use it to find y.

So, the solution of this system is (x,y) = (4,1)

y = x – 3

y = 4 – 3

y = 1

**Let’s solve one more system using a different method:**

5x – 3y = 17

__x + 3y = 11__

Notice that we have -3y in the first equation and +3y in the second. If we add these 2, we get zero, which means we lose variable y. So, we add these 2 equations and we get a linear equation with one variable.

5x – 3y + x + 3y = 17 – 11

6x = 6

__x = 1__

Now that we have x, we use it to find y.

5 – 3y = 17

-3y = 17 – 5

-3y = 12

y = 12/(-3)

y = -4

### Practice Questions

**1. Solve the system:**

1) (3,2)

2) (3,3)

3) (2,3)

4) (2,2)

**2. Solve the system:**

1) (0, -?5)

2) (0, ?5)

3) (-?5, 0)

4) (?5, 0)

**3. Find x and y from the following system of equations:**

1) (1,3)

2) (2,1)

3) (1,1)

4) (0,1)

**4. Find x and y from the following system of equations:**

*2x+3=y+6
*

*-4x-12=-8y*

1) (3,2)

2) (1,3)

3) (3,3)

4) (2,2)

**5. Solve the system, if a is some real number:**

**Written by**, Brian Stocker MA., Complete Test Preparation Inc.

**Date Published:**Thursday, November 27th, 2014

**Date Modified:**Monday, June 26th, 2023

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