Question

What are the solutions to the system of equations: \(6x + 5y = 19\) and \(4x - 6y = 10\)?

A. \((1, 2.6)\)

B. \((-1, 4)\)

C. \((1, 1)\)

D. \((4, -1)\)

Answer 1

To solve the system of equations, use the elimination method or substitution method. The solutions are approximately (2.9286, 0.2857).

Step-by-step explanation:

To find the solutions to the given system of equations, we can use the method of substitution or elimination. Let's use the elimination method.

Multiply the first equation by 4 and the second equation by 6 to make the coefficients of x in both equations equal:

24x + 20y = 76

24x - 36y = 60

Subtract the second equation from the first equation:

56y = 16

Divide both sides of the equation by 56:

y = 0.2857

Substitute the value of y into either of the original equations to find x:

4x - 6(0.2857) = 10

4x - 1.7142 = 10

4x = 11.7142

x = 2.9286

Therefore, the solutions to the system of equations are approximately (2.9286, 0.2857).