A classroom contains an equal number of boys and girls. If 1313 girls leave, twice as many boys as girls remain. What was the original number of students present?

5,252

Step-by-step explanation:

Let the number of boys present be b and the number of girls present be g

Now we are told these numbers are equal. This means b = g

Furthermore, if 1313 girls leave, the number of boys remaining would be twice the number of girls.

Mathematically, this can be expressed as follows:

b/(g-1313) = 2

b = 2(g-1313)

b = 2g - 2626

b + 2626 = 2g

We know that b = g from the initial equation, substituting this here yields:

g + 2626 = 2g

g = 2626

Since b = g, b = 2626 also

Total number of students = 2626 + 2626 = 5,252

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

(w – 2.5)(w + 2.5)

(–4v – 9)(–4v + 9)

step-by-step explanation: