Question

1. Solve and verify each of the following systems of linear equations.

/3 a. 5x – 2y =- 6 and 2x – y = 1

Answer:

/3 b. 2x + 3y = 432 and 5x – 2y = 16

Answer:

Answer 1

5x - 2y = -6 ⇒ 10x - 4y = -12
2x - 1y = 1 ⇒ 10x - 5y = 5
y = -17
5x - 2(-17) = -6
5x + 34 = -6
- 34 - 34
5x = -40
5 5
x = -8
(x, y) = (-8, -17)

2x + 3y = 432 ⇒ 10x + 15y = 2160
5x + 2y = 16 ⇒ 10x + 4y = 32
11y = 2128
11 11
y = 193.4545455
2x + 3(193.4545455) = 432
2x + 580.3636364 = 432
- 580.3636364 - 580.3636364
2x = -148.3636364
2 2
x = -74.1818182
(x, y) = (-74.1818184, 193.4545455)

Answer 2

A.

5x-2y= -6-------(1)

2x-y= 1------(2)

Equation (1) - 2 × Equation (2)

→5x-2y-4x+2y= -6 -2

Adding and Subtracting like terms

→x= - 8

Putting the value of x in equation 2

→2×(-8) -y =1

→-16 -y=1

Adding 16 on both sides of equation

→-y=16+1

→y = -17

x= -8, and y= -17

B

2x + 3y = 432------(3)

5x – 2y = 16---------(4)

2×Equation (3) + 3 × Equation (4)

→4x+6y+15x-6y=864+48

→19 x=912

Dividing both sides by 19, we get

x=48

Putting the value of x, in equation (3)

2× 48+3y=432

96+3y=432

3y=432-96

3y=336

Dividing both sides by,3 we get

y=112

Solution set is equal to, x=48,y=112