Answer: Infinite solutions.
Step-by-step explanation:
Plug the value of y into the second equation.
Add 12 on both sides.
Add 4x on both sides.
Any time you have a fraction within an equation, multiply the entire equation by the denominator to clear the fraction. Since the lead term is negative, we can multiply that away as well
(-14) (0=-1/14x²+4x+5) [now distribute]
0=x²-56x+70 [try to factor into binomials first]
Since 70 only has prime factors of 2·5·7, there is no combination which equals (-56). Use the quadratic formula, or complete the square. I'll use quadratic:
x=<u>-b+/-√(b²-4ac)</u>
2a
a=1, b=(-56), c=70
x= <u>-(-56)+/- √((-56)²-4(1)(70)</u>
2(1)
x= <u>56+/- √(3136-280)
</u> 2
<u />x=<u>56+/-√(2856)</u>
2
x=<u>56+/-√(2³·3·119)</u>
2
x=<u>56+/-2√(714)</u>
2
x=28+√714; x=28-√714
Given:
1 Van and 4 buses filled with 195 students.
1 Van and 5 buses filled with 241 students.
Let x and y be the number of students in Van and number of students in bus.
Subtract equation (1) from equation (2)
Substitute y=46 in equation (1)
Number of students that van can carry is 11.
Number of students that bus can carry is 46
