Question

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

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

Answer:

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