Solve by substitution -x+y=7 and 2x+3y=31

(2,9)

Step-by-step explanation:

To do this you have to solve one of the equations for a variable.

-x+y=7

2x+3y=31

Because the first equation doesn't have any numbers attached to the variables I decided to solve for the y in that equation.

-x+y=7

y=x+7

With this now one would have to plug this into the second equations:

2x+3(x+7)=31

Use the distributive property.

2x+3x+21=31

simplify.

5x+21=31

Isolate the x.

    -21     -21

5x=10

solve for the x.

x=2

Plug the x into one of the equations and solve for y.

-x+y=7

-2+y=7

isolate the y.

+2     +2

y=9

This  is the point of solution.

yes because they have the same amount of green and blur marbles.

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240