Question

Which is the solution to the system of equations? y = -1/3x - 11/2, 6x + y = -4

a) (x, y) = (-6, 0)
b) (x, y) = (-4, 2)
c) (x, y) = (-8, 0)
d) (x, y) = (-2, -2)

Answer 1

To solve the system of equations, substitute the value of y from the first equation into the second equation. Simplify the equation and combine like terms. Solve for x and substitute the value of x back into the first equation to find y.

Step-by-step explanation:

To find the solution to the system of equations, we need to solve them simultaneously. The given equations are:

y = -1/3x - 11/2

6x + y = -4

To solve this system, we can substitute the value of y from the first equation into the second equation:

6x + (-1/3x - 11/2) = -4

Simplifying this equation, we get:

6x - x/3 - 11/2 = -4

Combining like terms and simplifying further, we obtain:

17x/3 = 3/2

Multiplying both sides by 3/17, we find:

x = 9/17

Substituting this value of x back into the first equation, we get:

y = -1/3(9/17) - 11/2

y = -3/17 - 11/2

Simplifying this expression:

y = -93/34

Therefore, the solution to the system of equations is (x, y) = (9/17, -93/34).