Question

Solve the following system of equations: x − 2y = 14 x + 3y = 9 Select one: a. (1, 12) b. (−1, −12) c. (12, −1) d. (12, 1)

Answer 1

There are a few ways to solve system of equations. You could use the matrix approach but I am going to use elimination.

x − 2y = 14
x + 3y = 9

First I am going to times x + 3y = 9 by -1, which will turn the x into -x and allow use to eliminate the x and solve for y.

-1(x + 3y) = 9(-1)
-x - 3y = -9

Ok now that we have our new equation, lets use that.

x − 2y = 14
-x - 3y = -9
-------------------
0 -5y = 5
Get ride of the 0
-5y = 5
Divide out the -5
-5y / -5 = 5 / -5
y = - 1

Now that we have found y = -1 insert -1 in the equation x + 3y = 9 to find x

x + 3y = 9
x + 3(-1) = 9
x - 3 = 9
x = 9 + 3
x = 12

x = 12
y = -1
(x, y) = (12, -1) = c

Answer 2

We can solve this system of equation using substitution. We can start by getting the value of x from the equation x - 2y = 14. We can get the value of x here by adding 2y to each side, meaning that x = 2y + 14. Now we can substitute this into our other equation.

x - 3y = 9
(2y + 14) + 3y =9
5y + 14 = 9
5y - 14 + 14 = 9 - 14
5y = -5
y = -1.

Since the only answer that has y as negative one is C., that means that the answer is C., (12, -1).