System of equations, Help please!

Part 1: Explain, in complete sentences, how you would use the elimination method to solve the following system of equations. (4 points) Part 2: Provide the solution to the system. (2 points)

5x – 9y = –16
2x + 6y = –16


Part 1: Explain, in complete sentences, how you would use the substitution method to solve the following system of equations. (4 points) Part 2: Provide the solution to the system. (2 points)

x + 5y = 3
2x + 9y = 4

1) The system can be solved by multiplying the second equation by 3/2 and adding the result to the first equation. The sum will be an equation in x only, which can be solved by dividing by the x coefficient. The value of y is found by substituting the x value into either equation and solving for y.
.. (5x - 9y) + (3/2)(2x + 6y) = (-16) + (3/2)(-16)
.. 8x = -40 ... collect terms
.. x = -5 ... divide by 8
Using the second equation,
..2(-5)+6y = -16
.. 6y = -6 ... add 10
.. y = -1 ... divide by 6
The solution is (x, y) = (-5, -1).


2) To solve the system by substitution, solve the first equation for x and put the resulting expression in the second equation where x is. Solve that for y. Then use the expression for x to find the value of x by substituting the value of y into it.
.. x + 5y = 3
.. x = 3 - 5y ... first equation is solved for x
.. 2(3-5y) + 9y = 4 ... the expression is substituted for x
.. -y = -2 ... subtract 6, collect terms
.. y = 2 ... multiply by -1
.. x = 3 - 5(2) = -7
The solution is (x, y) = (-7, 2).

5x-2x-9y-6y
3x-15y= 0
3x= -15y
X= -5y
5x= -25y
-25y - 9y = -34y = -16
34y = 16
y = 16/34
X= -(5X16/34)= -40/7