Answer:
x = 0
Step-by-step explanation:
Multiply the first equation by -3 and add the second equation.
-3(-x +2y) +(6y) = -3(6) +(x +18)
3x -6y +6y = -18 +x +18 . . . . eliminate parentheses
3x = x . . . . . . . . .simplify
2x = 0 . . . . . . . . subtract x
x = 0 . . . . . . . . . .divide by 2
Answer: k = 4
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Explanation:
The piecewise function is essentially two different functions joined together. In this case,
h(x) = kx if 0 <= x < 1
OR
h(x) = x+3 if 1 <= x <= 5
The value of x determines which piece we use.
The two pieces will join together to be continuous only if the y value is the same for x = 1.
Plug x = 1 into the first piece and we get
h(x) = k*x
h(1) = k*1
h(1) = k
Do the same for the second piece
h(x) = x+3
h(1) = 1+3
h(1) = 4
Set the two results (k and 4) equal to each other and we get k = 4.
