Question

What is the value of y in the solution to the following system of equations?

2x + y = −4
5x + 3y = −6

Answer 1

x = -6, y = 8

Answer 2

if you have a texas instrument, its really easy to solve these. put them in a matrix. (2nd + x^-1 buttons), then scroll over to "edit" at the top, enter 2 x 3, then type in all your values which would look like this


2 1 -4
5 3 -6

then hit (2nd + mode) to exit. then go back to the matrix (2nd + x^-1) buttons and go over to math. press the option B, which is "rref(" and click enter. it'll enter that value, so go back to (2nd + x^-1) and select your matrix from that screen and hit enter. your new matrix will look like this:


1 0 -6
0 1 8

1 0; 0 1 are your multiplication values, just ignore those. -6 is your value for x, and 8 your value for y.

Answer 3

Substitution method :
2x + y = - 4 --> y = -2x - 4
now sub -2x - 4 in for y in the other equation
5x + 3y = - 6
5x + 3(-2x - 4) = - 6
5x - 6x - 12 = - 6
-x = - 6 + 12
-x = 6
x = - 6
now sub -6 in for x in either of the original equations
2x + y = - 4
2(-6) + y = - 4
- 12 + y = - 4
y = -4 + 12
y = 8
check...
2x + y = - 4
2(-6) + 8 = - 4
-12 + 8 = - 4
-4 = -4 (correct)
ANSWER : x = -6 and y = -4