Question

1. Solve and verify each of the following systems of linear equations. SHOW ALL WORK PLEASE AND THANK YOU

a. 5x – 2y =- 6 and 2x – y = 1
Answer:
b. 2x + 3y = 432 and 5x – 2y = 16
Answer:

Answer 1

Explanation:

(a)

Given the system of equation:

`5x-2y=-6` .....[1]

`2x-y=1` .....[2]

Multiply equation [2] by -2 we get;

`-4x + 2y = -2` ......[3]

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

`5x -2y+(-4x+2y) = -6-2`

`5x -2y-4x+2y= -6-2`

Combine like terms;

`x = -8`

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:

`2x+3y=432` .....[1]

`5x-2y=16` .....[2]

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

`15x -6y = 48` ......[3]

`4x +6y = 864` ......[4]

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

`15x -6y+4x+6y =48+864`

Combine like terms;

`19x = 912`

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

Answer: 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;

`2x+3y=432`

`2(48)+3(112)=432`

`96+33+3y=432`

`432=432` true

`5x-2y=16`

`5(48)-2(112)=16`

`240-224=16`

16 = 16 true