# Solve the following simultaneous equations. x + 3y = 2 , 2x + 8y = 6

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We have to solve the following set of simultaneous equations:

x + 3y = 2 ...(1)

2x + 8y = 6 ...(2)

2*(1) - (2)

=> 2x + 6y - 2x - 8y = 4 - 6

=> -2y = -2

=> y = -2/-2

=> y = 1

substitute in (1)

x + 3 = 2

=> x = 2 - 3

=> x = -1

**We get x = -1 and y = 1**

x + 3y = 2

x = 2 - 3y

plug it in as x into the other equation:

2(2 - 3y) + 8y = 6

4 - 6y + 8y = 6

bring like terms to the same side:

-6y + 8y = 6 - 4

combine:

2y = 2

divide by 2

y = 1x + 3(1) = 2

x + 3 = 2

subtract 3

x = 2 - 3

x = -1(-1 , 1)

x + 3y = 2

x = 2 - 3y

plug it in as x into the other equation:

2(2 - 3y) + 8y = 6

4 - 6y + 8y = 6

bring like terms to the same side:

-6y + 8y = 6 - 4

combine:

2y = 2

divide by 2

**y = 1**

now plug that into any of the problems:

x + 3(1) = 2

x + 3 = 2

subtract 3

x = 2 - 3

**x = -1**

**(-1 , 1)**

We'll solve the system using substitution method and we'll write x from the 1st equation, with respect to y:

x = 2 - 3y

We'll substitute x in the 2nd equation:

2(2 - 3y) + 8y = 6

We'll remove the brackets:

4 - 6y + 8y = 6

We'll combine like terms:

2y = 6 - 4

2y = 2

y = 1

We'll substitute y in the first equation:

x + 3 = 2

x = 2 - 3

x = -1

**The solution of the system is represented by the pair (-1 ; 1).**