John and his friends bought pastels, brushes, and canvases at an art supply store. The table shows the numbers of items bought and the amount each person spent. Identify the price of each item.

Cost of one canvas $1, one brush $2 and one pastel $3

Step-by-step explanation:

John and his friends bought pastels, brushes and canvases at an art supply store.

Let the price of each pastel represents by 'p', each brushes represents by 'b' and each canvas represents by 'c'.

John purchased 3 pastels, 4 brushes and 5 canvases for $22. The equation will be,

3p + 4b + 5c = 22 (1)

Robin purchased 2 pastels 5 brushes and 7 canvases for $23. The equation will be,

2p + 5b + 7c = 23(2)

Andrew purchased 4 pastels, 3 brushes and 6 canvases for $24. The equation will be,

4p + 3b + 6c = 24(3)

Now multiply equation (1) by 2 and equation (2) by 3.

6p + 8b + 10c = 44 (4)

6p + 15b + 21c = 69(5)

After subtracting from equation (5) to (4)

7b + 11c = 25 (6)

multiplying equation (2) by 2

4p + 10b + 14c = 46(7)

subtracting equation (3) from equation (7)

7b + 8c = 22

and subtracting from equation (6)

3c = 3

c = 1

putting the value of c in equation (6)

7b + 11(1) = 25

7b + 11 = 25

7b = 25 - 11

7b = 14

b = 2

Put the value of c and b in equation (1)

3p + 4(2) + 5(1) = 22

3p + 8 = 22 - 5

3p = 17 - 8

3p = 9

p = 3

Cost of one canvas $1, one brush $2 and one pastel $3.

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)