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 ( [tex]-\frac{1}{2}[/tex] , -2)
The point of intersection of the 2nd system is point (-1 , 3)
The point of intersection of the 3rd system is point ( [tex]-\frac{7}{3}[/tex] , [tex]\frac{5}{3}[/tex] )
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 = [tex]-\frac{1}{2}[/tex]
- Substitute the value of x in equation (1) or (2)
∵ y = 2( [tex]-\frac{1}{2}[/tex] ) - 1
∴ y = -1 - 1
∴ y = -2
∴ The solution of the 1st system is point ( [tex]-\frac{1}{2}[/tex] , -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 = [tex]-\frac{7}{3}[/tex]
- Substitute the value of x in equation (1) or (2)
∵ y = ( [tex]-\frac{7}{3}[/tex] ) + 4
∴ y = [tex]\frac{5}{3}[/tex]
∴ The solution of the 3rd system is point ( [tex]-\frac{7}{3}[/tex] , [tex]\frac{5}{3}[/tex] )
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)
