A student sketched some art on an 8.5 inch x 11 inch piece of paper. He wants to resize it to fit an 5 inch x 7 inch frame (as s
hown below)
What is the value of x? (Hint: Like Step #1 of the example in class)
A. x = 5
B. x = 6
C. x = 5.41
D. x = 7
What is the value of x? (Hint: Like Step #1 of the example in class)
A. x = 5
B. x = 6
C. x = 5.41
D. x = 7
1 answer:
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Answer:
The system of linear equations has infinitely many solutions
Step-by-step explanation:
Let's modified the equations and find the answer.
Using the first equation:
we can multiply by 2 in both sides, obtaining:
which can by simplified as:
which is equal to:
Considering the second equation:
Taking into account that from the first equation we know that: , we can express the second equation as:
, which can be simplified as:
Because (-8) is being divided by (2+k), then (2+k) can't be equal to 0, so:
if
This means that k can be any number different than -2, and for each of these solutions, there is a different solution for y, allowing also, different solutions for x.
For example, if k=0 then
which give us y=-4, and, because:
if y=-4 then
Now let's try with k=-1, then:
which give us y=-8, and, because:
if y=-8 then
.
Then, the system of linear equations has infinitely many solutions