Question

Solve the system of linear equations:

11x = 56 - y
3x = 28 + y

Options:
a) x = 4, y = 32
b) x = 6, y = 40
c) x = 8, y = 24
d) x = 10, y = 16

Answer 1

To solve the system of linear equations, multiply the equations by appropriate values to eliminate one of the variables, and then solve for the remaining variable. In this case, multiplying the equations by 3 and 11 allows us to eliminate the variable y. Substituting the value of y into one equation gives us the solution: x = 6 and y = -10.

Step-by-step explanation:

To solve the system of equations, we can start by eliminating one of the variables. Let's eliminate the variable y. We can do this by multiplying both sides of the first equation by 3 and the second equation by 11:

33x = 168 - 3y

33x = 308 + 11y

Next, we can subtract the second equation from the first equation:

33x - 33x = 168 - 3y - (308 + 11y)

0 = -140 - 14y

Simplifying further, we get:

14y = -140

y = -10

Now we can substitute the value of y into one of the original equations. Let's use the first equation:

11x = 56 - (-10)

11x = 66

x = 6

Therefore, the solution to the system of equations is x = 6 and y = -10.