Question

Solve the below system of equations using the best method. Please describe the method used [substitution, graphing, elimination, etc], and give your answer in the form (x,y).
1.) 5x - 2y = -1
8x + 4y = 56

2.) 3x - y = -16
-4x - y = 21

Answer 1

1). Since you have -2y and 4y, elimination is easy to do for solving for x..
Keep the first equation and multiply the second equation by 2. Then add.

5x - 2y = -1
8x + 4y = 56

10x - 4y = -2
8x + 4y = 56
-----------------
18x       = 54

x = 3

Now we can use substitution to solve for y.
Substitute 3 for x in the first original equation and solve for y.

5x - 2y = -1

5(3) - 2y = -1

15 - 2y = -1

-2y = -16

y = 8

(3, 8)


2.)

3x - y = =16
-4x - y = 21

Multiply both sides of the first equation by -1 to change all signs. Then when you add the equations, you eliminate y and solve for x.

-3x + y = 16
-4x - y = 21
-----------------
-7x       = 37

x = -37/7

Now multiply the first original equation by 4 and the second original by 3 to eliminate x and solve for y.

 12x - 4y = -64
-12x - 3y =  63
---------------------
         -7y   = -1

y = 1/7

Solution: (-37/7, 1/7)