Answer:
68%
Step-by-step explanation:
By using a scientific calculator
IF:
|1/2.x -2/3.y = 7 and
|a.x - 8.y = -1
have no solution, that means these 2 linear equations ARE PARALLEL (since they can never meet). Reminder: 2 equations are parallel if they have the same coefficient , so let write each of the equation in the normal form:
a)1/2.x -2/3.y = 7→ -2/3.y = -1/2.x + 7 → y = 3/4.x - 21/2
b) a.x - 8.y = -1 → - 8.y = -a.x - 1 → y= a/8.x + 1
a) and b) are // if (3/4) = (a/8), [the 2 coefficient OR the 2 slopes)
a/8 = 3/4 → a = 24/4 and a = 6 (Answer D)
I would need a bit more to answer that one my friend
Answer:
g(x) = (1/2)x + 3
f(x) = g(x) at (-1/2 , 13/4)
Step-by-step explanation:
g(x) and f(x) will have exactly one solution when they are not parallel (same slope) and when they are not equivalent functions (like doubling or halving all terms).
f(x) = (-5/2)x - 3
g(x) = (1/2)x + 3 <= choose an easy equation.
To find the solution, equate the two functions:
f(x) = g(x)
(-5/2)x - 3 = (1/2)x + 3
(-5/2)x - (1/2)x = 3 + 3 <= move variables to one side, constants to other
(-6/2)x = 6 <= simplify
x = 6 / (-6/2) <=isolate x
x = -6/12
x = -1/2
Substitute x = -1/2 into any equation to find y
g(x) = (1/2)x + 3
g(1/2) = (1/2)(1/2) + 3
g(1/2) = (1/4) + 3
g(1/2) = (1/4) + (12/4) <= find common denominator to add
y = (13/4) <= the function symbol can be replaced by y
The coordinates are (-1/2 , 13/4).
