Question

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

Answer 1

Answer:

Step-by-step 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