Match each point of intersection with the system of equations whose solution is at that point. W X Y Z y = -2x − 3 y = 2x − 1 arrowRight y = x + 4 y = -x + 2 arrowRight y = -2x − 3 y = x + 4 arrowRight y = 2x − 1 y = -x + 2 arrowRight

The points W, X, Y, Z are missing but we can find them when we solve each system of equations

The point of intersection of the 1st system is point ( , -2)

The point of intersection of the 2nd system is point (-1 , 3)

The point of intersection of the 3rd system is point ( , )

The point of intersection of the 4th system is point (1 , 1)

Step-by-step explanation:

The 1st system is:

y = -2x - 3 ⇒ (1)

y = 2x - 1 ⇒ (2)

Equate (1) and (2)

∴ 2x - 1 = -2x - 3

- Add 2x to both sides

∴ 4x - 1 = - 3

- Add 1 to both sides

∴ 4x = -2

- Divide both sides by 4

∴ x =

- Substitute the value of x in equation (1) or (2)

∵ y = 2( ) - 1

∴ y = -1 - 1

∴ y = -2

∴ The solution of the 1st system is point ( , -2)

The 2nd system is:

y = x + 4 ⇒ (1)

y = -x + 2 ⇒ (2)

Equate (1) and (2)

∴ x + 4 = -x + 2

- Add x to both sides

∴ 2x + 4 = 2

- Subtract 4 from both sides

∴ 2x = -2

- Divide both sides by 2

∴ x = -1

- Substitute the value of x in equation (1) or (2)

∵ y = -1 + 4

∴ y = 3

∴ The solution of the 2nd system is point (-1 , 3)

The 3rd system is:

y = -2x - 3 ⇒ (1)

y = x + 4 ⇒ (2)

Equate (1) and (2)

∴ x + 4 = -2x - 3

- Add 2x to both sides

∴ 3x + 4 = - 3

- Subtract 4 from both sides

∴ 3x = -7

- Divide both sides by 3

∴ x =

- Substitute the value of x in equation (1) or (2)

∵ y = ( ) + 4

∴ y =

∴ The solution of the 3rd system is point ( , )

The 4th system is:

y = 2x - 1 ⇒ (1)

y = -x + 2 ⇒ (2)

Equate (1) and (2)

∴ 2x - 1 = -x + 2

- Add x to both sides

∴ 3x - 1 = 2

- Add 1 to both sides

∴ 3x = 3

- Divide both sides by 3

∴ x = 1

- Substitute the value of x in equation (1) or (2)

∵ y = -1 + 2

∴ y = 1

∴ The solution of the 4th system is point (1 , 1)

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.