(4,-2) and (2,-8) lie on the line Ax-2By = 28. What is the value of A?
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4,-2) and (2,-8) lie on the line Ax-2By = 28. What is the value of A?
Put the points in. First one.
A4-2B(-2)=28
4A+4B=28
A+B=7 call this equation 1)
second point:
A2-2B(-8)=28
2A+16B=28
A+8B=14 call this equation 2)
Now you have two equations...
A+B=7
A+8B=14
Now solve for A and B by any number of methods.
To find the value of A, we can solve the system of equations using either substitution or elimination method. Let's use the elimination method to solve this system.
First, we'll multiply equation 1 by 8 to make the coefficient of B in equations 1 and 2 equal. This will allow us to eliminate B:
8(A + B) = 8(7)
8A + 8B = 56 (equation 1 multiplied by 8)
Next, we'll subtract equation 2 from the equation we just obtained:
(8A + 8B) - (A + 8B) = 56 - 14
Simplifying it further, we get:
7A = 42
Now we can solve for A by dividing both sides by 7:
A = 6
Therefore, the value of A is 6.