Final answer:
To solve the system of equations, we can use the method of elimination. Multiply the second equation by 2 to eliminate the x terms, then add the two equations to eliminate the x terms. Solve for y and substitute the value of y into one of the original equations to solve for x. The solution is x = -2.75 and y = 7.25.
Step-by-step explanation:
To find the solution of the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:
Step 1: Multiply the second equation by 2 to eliminate the x terms. The new equation becomes -20x + 10y = 100.
Step 2: Add the two equations together to eliminate the x terms. We get 16y = 116.
Step 3: Solve for y by dividing both sides of the equation by 16. The solution is y = 7.25.
Step 4: Substitute the value of y into one of the original equations to solve for x. Let's use the first equation: 10x + 6(7.25) = 16. Simplifying the equation gives 10x + 43.5 = 16. Subtracting 43.5 from both sides gives 10x = -27.5. Dividing both sides by 10 gives x = -2.75.
Therefore, the solution to the system of equations is x = -2.75 and y = 7.25.