a. Solve by using substitution or elimination:
   3x + 2y = -12  and  2x + y = -7
b. Solve as above:
   2x - 4y = -2  and  4x + 8y = 0
c. Solve as above:
   X  - 2y = 9  and  3x + 2y = -5
d. Solve by using substitution and elimination:
   x = 3y + 11  and  2x + 5y = 0

Hi teatea,

I will use the same format as last time. Give you a few pointers, then
leave lots of space between the answers.

a. 3x + 2y = -12     2x + y = -7

Substitution involves expressing one unknown in function of the other unknown.
Lets express y in function of x by using the second equation. We have:



















3x + 2y = -12     y = -7 - 2x
We then replace y in the first expression with the value of y in the second.













3x + 2*(-7 - 2x) = -12     y = -7 - 2x
The left expression will give us x, we then replace that value in the
right expression.















3x  - 14 - 4x = -12     y = -7 - 2x
-x = 2                  y = -7 + 2*2
x = -2                  y = -3



b. In this one we'll use elimination.
Elimination works as follows:
If you have expressions you can multiply them by real numbers and get
an equivalent expression. You can also add two expressions.

We have:
2x - 4y = -2     4x + 8y = 0
Multiply the second one by 1/2













2x - 4y = -2     2x + 4y = 0
Now add the right one to the left one.

















4x = -2     2x + 4y = 0
x = -1/2    -1 + 4y =0
x = -1/2     y = 1/4



c.  x - 2y = 9    3x + 2y = -5
You must have gotten the gist of it now.
x = 9 + 2y   3x + 2y = -5

x = 9 + 2y   27 + 6y + 2y = -5

x = 9 + 2y   8y = -32
x = 9 + 2y    y = -4
x = 9 - 8     y = -4
x = 1         y = -4

d.  x = 3y + 11  and  2x + 5y = 0
substitution:
x = 3y + 11    2*(3y+11) + 5y =0
x = 3y + 11     6y + 22 + 5y =0
x = 3y + 11     11y = -22
x = 3y +11        y = -2
x = -6 +11        y = -2
x = 5             y = -2

elimination
x = 3y + 11      2x + 5y =0
x - 3y = 11      2x + 5y =0
-2x + 6y = -22   2x + 5y =0
-2x + 6y = -22    11y = -22
-2x + 6y = -22      y = -2
-2x - 12 = -22      y = -2
-2x = -10           y = -2
x = 5               y = -2


I hope this answers your question. If you need any more help or
clarifications please do not hesitate to ask.

Thanks.
endo