Question

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

Answer 1

The answers to the question are

1.) y = -2x − 3 / y = 2x − 1 --> Z

2.) y = x + 4 / y = -x + 2 --> X

3.) y = -2x − 3 / y = x + 4 --> W

4.) y = 2x − 1 / y = -x + 2 --> Y

Answer 2

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

Answer:

The point of intersection of the 1st system is point ( $-\frac{1}{2}$ , -2)

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

The point of intersection of the 3rd system is point ( $-\frac{7}{3}$ , $\frac{5}{3}$ )

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 = $-\frac{1}{2}$

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

∵ y = 2( $-\frac{1}{2}$ ) - 1

∴ y = -1 - 1

∴ y = -2

∴ The solution of the 1st system is point ( $-\frac{1}{2}$ , -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 = $-\frac{7}{3}$

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

∵ y = ( $-\frac{7}{3}$ ) + 4

∴ y = $\frac{5}{3}$

∴ The solution of the 3rd system is point ( $-\frac{7}{3}$ , $\frac{5}{3}$ )

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)