what is the solution of the following linear system?
-4x - y = 5
-12x - 3y = 15
a) (-2,1)
b) none
c) (3,-2)
d) infinite number of solutions
Multiply the first equation by 3 to find that the equations are the same. What does that tell you?
To find the solution to the given linear system of equations, we can solve it using the method of substitution or elimination. Let's use the method of elimination.
First, let's multiply the first equation by -3 to make the coefficients of "y" in both equations the same:
(1) -3 * (-4x - y) = -3 * 5
-12x + 3y = -15
Now we have the following two equations:
-12x + 3y = -15 (2)
-12x - 3y = 15 (3)
Next, we can eliminate the x-coefficient by subtracting equation (3) from equation (2):
(-12x + 3y) - (-12x - 3y) = -15 - 15
-12x + 3y + 12x + 3y = -30
6y = -30
Dividing both sides of the equation by 6, we get:
y = -5
Now, substitute the value of y into any of the original equations to solve for x. Let's use the first equation:
-4x - (-5) = 5
-4x + 5 = 5
-4x = 5 - 5
-4x = 0
x = 0/(-4)
x = 0
So the solution to the given linear system of equations is x = 0 and y = -5.
Therefore, the correct answer is (0, -5).