Question

Imagine that yourfriend missed the lesson on how to solve a system of equations using the substitution method. You want to help him or her catch up in their math class, so you decide to write an email describing what they missed. Write an email to your friend including:
An explanation of what a system of equations is
A general description of how to use the substitution method
An example of a system of equations
Your solution steps and explanations including the substitution method
Your final answer for the system

Answer 1

A system of equations is a collection of two or more equations with the same variables. When solving this system, u need to find the unknown variables. One way of solving a system of equations is by substitution. 

example :

2x + 2y = 6 (equation 1)
3x + y = 4 (equation 2)

we need to pick a variable and isolate it. The easiest one to pick since it is already by itself is the y in the second equation.
3x + y = 4.....subtract 3x from both sides
y = -3x + 4

now we can sub -3x + 4 in for y in the 1st equation...u have to make sure u sub it back into the 1st equation and not the same equation u used to find it.

2x + 2y = 6.....sub in -3x + 4 in for y and solve for x
2x + 2(-3x + 4) = 6...distribute thru the parenthesis
2x - 6x + 8 = 6...subtract 12 from both sides
2x - 6x = 6 - 8...simplify
-4x = -2...divide both sides by -4
x = -2/-4
x = 1/2

now that we have a numerical number for x, u can sub this back into either of ur equations to find a numerical answer for y.

y = -3x + 4...when x = 1/2
y = -3(1/2) + 4
y = -3/2 + 4
y = -3/2 + 8/2
y = 5/2

so ur solution is : (1/2,5/2) <===

and u can check ur answers by subbing them into ur equations to see if they satisfy both equations...because for it to be a solution to this system, it has to satisfy both equations and not just one of them