Final answer:
To solve the system of equations by elimination, we need to eliminate one variable by adding or subtracting the two equations. However, for both systems given, we cannot eliminate any of the variables. Hence, these systems cannot be solved by elimination.
Step-by-step explanation:
To solve the system of equations by elimination, we need to eliminate one variable by adding or subtracting the two equations. Let's consider the first system of equations:
a) 3x + 5y = 10
b) -4x - 3y = 9
To eliminate the variable x, we can multiply equation (a) by 4 and equation (b) by 3, resulting in:
a) 12x + 20y = 40
b) -12x - 9y = 27
Now, add equation (a) and equation (b) together:
12x + 20y + (-12x - 9y) = 40 + 27
11y = 67
Since we cannot eliminate the variable y, this system of equations cannot be solved by elimination.
For the second system of equations:
a) 2x + ay = 4
b) bx + 7y = 2
To eliminate the variable x, we can multiply equation (a) by b and equation (b) by 2, resulting in:
a) 2bx + aby = 4b
b) 2bx + 14y = 4
Now, subtract equation (a) from equation (b):
(2bx + 14y) + (-2bx - aby) = 4 - 4b
14y - aby = 4 - 4b
Since we cannot eliminate the variable y, this system of equations cannot be solved by elimination.