a x + b y = 72 6 x + 2 b y = 56 In the given system of

Question

a x + b y = 72 6 x + 2 b y = 56 In the given system of equations, a and b are constants. The graphs of these equations in the xy -plane intersect at the point 4 , y . What is the value of a ?

Accepted Answer

Choice D is correct. It&rsquo;s given that the graphs of the given system of equations intersect at the point 4 , y . Therefore, 4 , y is the solution to the given system. Multiplying the first equation in the given system by - 2 yields - 2 a x - 2 b y = - 144 . Adding this equation to the second equation in the system yields - 2 a + 6 x + - 2 b + 2 b y = - 144 + 56 , or - 2 a + 6 x = - 88 . Since 4 , y is the solution to the system, the value of a can be found by substituting 4 for x in this equation, which yields - 2 a + 6 4 = - 88 . Dividing both sides of this equation by 4 yields - 2 a + 6 = - 22 . Subtracting 6 from both sides of this equation yields - 2 a = - 28 . Dividing both sides of this equation by - 2 yields a = 14 . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.

Question a-x-b-