1. solve and verify each of the following systems of linear equations. show all work and you a. 5x – 2y =- 6 and 2x – y = 1 b. 2x + 3y = 432 and 5x – 2y = 16

Step-by-step explanation:

(a)

Given the system of equation:

               .....[1]

                   .....[2]

Multiply equation [2] by -2 we get;

        ......[3]

Add equation [1] and [3] to eliminate y and solve for x we have;

Combine like terms;

Substitute the value of x in [2] we get;

2(-8)-y =1

-16-y = 1

Add 16 both sides we get;

-y = 17

or

y =-17

Answer; Solution for the given system of equation is (-8, -17)

Verify:

Substitute the value of x = -8 and y = -17 in the system of equation;

5x -2y = -6

5(-8)-2(-17) = -6

-40+34 = -6

-6 = -6          True

2x-y =1

2(-8)-(-17) = 1

-16+17 = 1

1 = 1               True.

(b)

Given the system of equation:

               .....[1]

                   .....[2]

Multiply equation [2] by 3 and equation [1] by 2 we get;

        ......[3]

        ......[4]

Add equation [3] and [4] to eliminate y and solve for x we have;

Combine like terms;

Divide both sides by 19 we get

x = 48

Substitute the value of x in [2] we get;

5(48)-2y=16

240 -2y = 16

Subtract 240 from both sides we get;

-2y =-224

Divide both sides by -2 we get

y =112

Solution for the given system of equation is (48, 112)

Verify:

Substitute the value of x = 48 and y = 112 in the system of equation;

        true

16 = 16                          true