Final answer:
The solution to the system of equations is x = 43/22 and y = (16/11)(43/22) - (6/11).
Step-by-step explanation:
To solve the system of equations using elimination, we want to eliminate one of the variables by manipulating the equations. In this case, we can eliminate the variable x. We will multiply equation 2 by 4 to make the x-coefficients the same:
1. 4x - 9y = 14
2. -20x + 20y = -20
Now, add equation 1 and equation 2:
4x - 9y + (-20x + 20y) = 14 + (-20)
Simplifying:
-16x + 11y = -6
This gives us a new equation in terms of x and y. We can solve this equation by isolating one variable:
-16x + 11y = -6
Isolating y:
11y = 16x - 6
y = (16/11)x - (6/11)
Now we have the value of y in terms of x. To find the value of x, we can substitute this expression for y into one of the original equations. Let's substitute into equation 1:
4x - 9((16/11)x - (6/11)) = 14
Simplifying:
4x - (144/11)x + (54/11) = 14
Combining like terms:
(44/11)x = 14 - (54/11)
Simplifying:
(44/11)x = 140/11 - 54/11
(44/11)x = 86/11
Dividing both sides by (44/11):
x = 86/11 ÷ (44/11)
Simplifying:
x = 86/11 * (11/44)
x = 86/44
Simplifying:
x = 43/22
Therefore, the solution to the system of equations is: x = 43/22 and y = (16/11)(43/22) - (6/11)