If-5x-3y = 4 and 6x – 4y = 2 are true equations, what would be the value of 11x - y?
To find the value of 11x - y, we need to find the values of x and y that satisfy both equations.
First, let's solve the system of equations:
-5x - 3y = 4 ...(1)
6x - 4y = 2 ...(2)
We can multiply equation (1) by 6 and equation (2) by -5 to eliminate the y variable:
-30x - 18y = 24 ...(3)
-30x + 20y = -10 ...(4)
Now, if we subtract equation (4) from equation (3), we can eliminate the x variable:
-30x - 18y - (-30x + 20y) = 24 - (-10)
-30x + 30x - 18y - 20y = 24 + 10
-38y = 34
y = -34/38
y = -17/19
To find the value of x, we can substitute the value of y in equation (1):
-5x - 3(-17/19) = 4
-5x + 51/19 = 4
-5x = 4 - 51/19
-5x = (76 - 51)/19
-5x = 25/19
x = -25/19 * 1/5
x = -25/95
x = -5/19
Now that we have the values of x and y, we can find the value of 11x - y:
11x - y
= 11(-5/19) - (-17/19)
= -55/19 + 17/19
= (-55 + 17)/19
= -38/19
Therefore, the value of 11x - y is -38/19.