8. Let f(x) = 3x + 2 and g(x) = x - 3. Find f(x) - g(x) and state its domain.
1 answer:
You might be interested in
Answer:
Pilar is correct. Both systems have solution (-2, 4).
Step-by-step explanation:
Graphing, or any other means of solving these systems of equations reveals both systems have the same solution: (x, y) = (-2, 4).
_____
By Cramer's rule, the solution to the first set is ...
x = (2(6)-4(2))/(2(5)-4(3)) = 4/-2 = -2
y = (2(5)-6(3))/-2 = -8/-2 = 4
(x, y) = (-2, 4) is the solution to the first system
__
Since the first equation of the second system is the same as the first equation of the first system, we know the above solution satisfies that equation. We only need to check to see if the same point satisfies the second equation of the second system:
11(-2) +8(4) = -22 +32 = 10 . . . . . yes,
(-2, 4) is the solution of the second system
Pilar is correct that both systems have the same solution.
_____
Cramer's Rule tells you the solution to
- ax +by = c
- dx +ey = g
is ...
- x = (bg -ec)/(bd -ea)
- y = (cd -ga)/(bd -ea) . . . . same denominator as for x
I like to use Cramer's Rule when the solution is needed without a lot of steps. Here, we could use the Elimination method to eliminate the y-variable and solve for x. Then more steps are needed to find y. The writing out and explanation are tedious, so it is much simpler just to use a formula that gives the answer.
