Abag contains green marbles and blue marbles, 40 in total. the number of green marbles is 7 more than 2 times the number of blue marbles. how many green marbles are there?

There are 29 green marbles.

Step-by-step explanation:

x: green marbles

y: blue marbles

So we have an equation:

x + y = 40

while,

2y = x - 7

so set this equation equal to x, we have

x = 2y + 7

replace x into 2y + 7 for the first equation

and this is how it looks:

(2y + 7) + y = 40

2y + y = 40 - 7

3y = 33

y = 11

x = 40 - y

x = 40 - 11

x = 29

(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