Answer: The answer to number 2 is letter c.
Explanation:
First solve the system of equations.
4x+3y=10.
-6x-5y=-16
Get one of the tow variables the same number but opposite sign by multiplying the first equation by three and the second equation by 2.
12x+9y=30
-12x-10y=-32
Add the equations together.
-y=-2
Simplify.
y=2
Plug in y in one of the equations and solve.
4x+3(2)=10
Multiply.
4x+6=10
Isolate the variable.
4x=10-6
Subtract.
4x=4
Simplify.
x=1
Plug the x and y values of 1 and 2 into the options provided and which ever one comes out true is the answer.
Answer to number 1
Answer: The system of equations for the first problem is
8v + 8b = 240
4v + 1b= 54
and the are 8 kids on each van and 22 kids on each bus.
Step by step explanation:
To make the system of equations. You know that 240 kids are going to be seated between 8 vans and 2 busses so 8 times the number of kids on one van plus 8 times the number of kids on one bus must equal 240. So...
8v + 8b = 240.
You also know that 54 kids are going to be seated between 4 vans and 1 bus. So the 4 times the number of kids on one van plus one times the number of kids on one bus must equal 54. So...
4v + 1b = 54
First make one of the two coefficients the same number but opposite sign.
8v + 8b = 240
-8v - 2b = -108
Then add together.
6b = 132.
Simplify
b = 22
Then plug into one of the two equations and solve.
4v + 1(22) = 54
Multiply.
4v + 22 = 54
Isolate the variable.
4v = 54 - 22
Subtract.
4v = 32
Simplify.
v = 8