Hey everyone it's Angelique,

Today class we learned the second method for solving systems of linear equations of 2 equations and 2 unknowns which is substituting.

the steps for solving 2 equations, 2 unknowns using this method are :

1. Solve one of the equations for one of the variables2. Substitute this equation into the other equation and sold for the second variable3. Substitute this value into either equation and solve for the first variable4. State the answer as an ordered pair5. Check

For Example:

using the equations -4x + y = 1
                             3x + 2y + 8 = 0

you would chose one of the equations and solve for one of the variables, I'm going to use the first equation as and example for Step 1:

-4x + y = 1 would be changed to y = -4x + 1 and is now solved for y

Step 2:
now you would take the value of y which is (-4x +1) and substitute it into the second equation to solve for the second variable which is x, like so:

3x + 2y + 8 = 0

3x + 2 (-4x +1) + 8 = 0

now you distribute making the equation:

3x - 8x + 2 + 8 = 0

and then combine like terms :

-5x + 10 = 0

then get the variable on one side by itself and bring the constant to the other side of the equals sign:

-5x = -10

now divide both sides by the coefficient to get x by itself:

-5x      -10 
-5    =   -5

and now divide the constant by the same thing to get your answer for x:

x = 2  ---> x = 2
      1

Step 3 :
Now that we have found the value of x in the first step its on to the second step where we'll be using the value of x to find the value of y :

4x + y = 1

4(2) + y = 1

8 + y = 1

now take the constant over to the other side:

y = 1 - 8

y = -7

and now you have found the value y this lead to Step 4:
which is stating the ordered pair which is (2, -7)

Step 5:
lastly we will be using the values of x and y that we solved for which is (2, -7) and substitute it back into the original equations

equation 1:
4x + y = 1
4(2) + (-7) = 1
8- 7 = 1
1 = 1

equation 2:
3x + 2y + 8 = 0
3(2) + 2 (-7) + 8 = 0
6 - 14 + 8 = 0
0 = 0

the values for x and y work out in both the checks so it's correct !

HOMEWORK:Don't forget to do the handout Solving Systems of Linear Equations : Two Equations, Two Unknowns

Hope you have a great night ! :)