use elimination method to solve.
A+6b=14
A+2b=2 does it have (a)one solution
(b)Infin. many sol
(c)no solution
a + 6 b = 14
- a - 2 b = - 2
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6 b - 2 b = 14 - 2
4 b = 12 Divide both sides by 4
b = 12 / 4
b = 3
a + 6 b = 14
a + 6 * 3 = 14
a + 18 = 14
a = 14 - 18
a = - 4
is the answer one solution
To solve the system of equations using the elimination method, we need to eliminate one variable by manipulating the equations in a way that the coefficients of one of the variables become the same or opposite.
Given the system of equations:
1) A + 6b = 14
2) A + 2b = 2
To eliminate variable A, we can subtract equation 2 from equation 1. By doing this, the A term will cancel out, leaving us with an equation in terms of b:
(A + 6b) - (A + 2b) = 14 - 2
6b - 2b = 12
4b = 12
b = 12/4
b = 3
Now that we have the value of b, we can substitute it back into either equation 1 or 2 to solve for the value of A. Let's use equation 2:
A + 2(3) = 2
A + 6 = 2
A = 2 - 6
A = -4
Therefore, the solution to the system of equations is A = -4 and b = 3.
Now, let's determine the number of solutions:
Since we have obtained specific values for both variables A and b, the system has a unique solution. So the answer is:
(a) one solution.