Question

(4y + 3)
(5x - 7)
(3x + 17°
X= ,y= ,

Answer 1

The value of x = 12, the value of y = 31

How to solve for x and y

These angles (4y + 3) and (5x - 7) are on a straight line. Hence they would be equal to 180 degrees

(4y + 3) + (5x - 7) = 180

when we simplify the equation above we would have

4y + 5x = 184

The basis of this is that : Alternate angles (called Z-angles) are always equal. while Corresponding angles (called F-angles) are always equal.

These angles (5x - 7) and (3x + 17) are alternate hence they are equal

(5x - 7) = (3x + 17)

2x = 24

x = 12

Put the value of x in 4y + 5x = 184

4y + 5 * 12 = 184

4y + 60 = 184

4y = 124

y = 124 / 4

y = 31

Hence the value of x = 12, the value of y = 31

question

The complete diagram is in the attachment

Answer 2

Simplifying

4y + 3 = 5x + -7 + 3x + 17

Reorder the terms:

3 + 4y = 5x + -7 + 3x + 17

Reorder the terms:

3 + 4y = -7 + 17 + 5x + 3x

Combine like terms: -7 + 17 = 10

3 + 4y = 10 + 5x + 3x

Combine like terms: 5x + 3x = 8x

3 + 4y = 10 + 8x

Solving

3 + 4y = 10 + 8x

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-3' to each side of the equation.

3 + -3 + 4y = 10 + -3 + 8x

Combine like terms: 3 + -3 = 0

0 + 4y = 10 + -3 + 8x

4y = 10 + -3 + 8x

Combine like terms: 10 + -3 = 7

4y = 7 + 8x

Divide each side by '4'.

y = 1.75 + 2x

Simplifying

y = 1.75 + 2x

i hope that helps