Answer:
(a) To solve a system of equations using elimination, we can eliminate one of the variables by adding or subtracting the equations. In this case, we can add the two equations to eliminate the variable y:
x - y = 11
2x + y = 19
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3x = 30
Dividing both sides of the equation by 3, we find that x = 10. We can then substitute this value into one of the original equations to find the value of y:
x - y = 11
10 - y = 11
-y = 1
y = -1
Therefore, the solution to the system of equations is x = 10 and y = -1. Answer: (10, -1).
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(B)
To solve this system by elimination, we need to eliminate one of the variables by adding or subtracting the two given equations. Let's first multiply the first equation by 2 to obtain:
2 * (x - y = 11)
2x - 2y = 22
Next, we add this equation to the second given equation to eliminate the variable y:
2x - 2y + 2x + y = 22 + 19
3x - y = 41
We can now solve for x by dividing both sides of the equation by 3:
3x - y = 41
(3x - y) / 3 = 41 / 3
x = 14
We can now substitute this value for x in either of the original equations to solve for y. Let's use the second equation:
2x + y = 19
2 * 14 + y = 19
28 + y = 19
y = -9
Therefore, the solution to the system of equations is x = 14 and y = -9.