Question

Consider this system of equations.

x + 2y = 13
12x + 5y = -4

a. (3, -5)
b. (-2, 3)
c. (1, -3)
d. (5, 2)

Answer 1

To solve the system of equations x + 2y = 13 and 12x + 5y = -4, we can use the method of substitution or elimination. I will use the method of substitution. The solution to the system of equations is approximately (x, y) = (-3.84, 8.42).

Step-by-step explanation:

To solve the system of equations x + 2y = 13 and 12x + 5y = -4, we can use the method of substitution or elimination. I will use the method of substitution.

Step 1: Solve one of the equations for one variable. From the first equation, we can solve for x:
x = 13 - 2y

Step 2: Substitute the value of x into the second equation:
12(13 - 2y) + 5y = -4

Step 3: Simplify and solve for y:
156 - 24y + 5y = -4
-19y = -160
y = (-160)/(-19) = 8.42 (approx)

Step 4: Substitute the value of y back into the first equation to find x:
x = 13 - 2(8.42)
x = -3.84 (approx)

So the solution to the system of equations is approximately (x, y) = (-3.84, 8.42).