Before viewing this page, it would be helpful to learn how to Solve Simultaneous Equations By Graphing.

The purpose of solving simultaneous equations is to find the **same x-value** and the **same y-value** that satisfies both equations.
To solve, one term from one equation is **substituted** into the other equation.

Solve these two equations by substitution:

y = x + 6

x = –2y

**Answer:**
*The x value and the y value are the same in both equations.
In the second equation, x is equal to –2y, so we will substitute –2y for x into the first equation.*

y = x + 6

y = –2y + 6

y + 2y = 6

3y = 6

y = 2

*Now, we'll find the x value by substituting y = 2 into either equation.*

y = x + 6

2 = x + 6

x = 2 – 6

x = –4

The simultaneous solution for both equations is x = –4 and y = 2.

Solve these two equations by substitution:

y = 3x – 4

x = y + 2

**Answer:**
*The x value and the y value are the same in both equations.
In the second equation, x is equal to (y + 2), so we will substitute (y + 2) for x into the first equation.
Be careful to use brackets.*

y = 3x – 4

y = 3 (y + 2) – 4

y = 3y + 6 – 4

y = 3y + 2

y – 3y = 2

–2y = 2

y = –1

*Now, we'll find the x value by substituting y = –1 into either equation.
The second equation looks the easiest.*

x = y + 2

x = –1 + 2

x = 1

The simultaneous solution for both equations is x = 1 and y = –1.

Solve these two equations by substitution:

y = 2x + 1

y = x + 3

**Answer:**
*The x value and the y value are the same in both equations.
In the first equation, y is equal to 2x + 1. In the second equation, y is equal to x + 3.
Since both are equal to y, they are equal to each other.*

2x + 1 = x + 3

2x – x = 3 – 1

x = 2

*Now, we'll find the y value by substituting x = 2 into either equation.
The second equation looks the easiest.*

y = x + 3

y = 2 + 3

y = 5

The simultaneous solution for both equations is x = 2 and y = 5.

y = 4x + 1

x = y + 2

**Answer**

x = –1

y = –3