Use the substitution method to solve the system of equations.
3x + 4y = 10
y= x-1

x = 2, y = 1

Step-by-step explanation:

3x + 4y = 10

y = x - 1

The value of y is given, so plug in (x - 1) for y in the first equation:

3x + 4(x - 1) = 10

Expand:

3x + 4x - 4 = 10

Simplify:

7x - 4 = 10

Add 4 to both sides:

7x = 14

Divide both sides by 7:

x = 2

Plug in 2 for x in the second equation:

y = 2 - 1

y = 1

(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

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.