Respuesta :

The correct answer is A = 110, B= 40, C=20..

Explanation

If A+B-C= 170 and B+C-A=130 ,  

=C+A = 130

or, C= 130- A

Again, A+B-C =170

or, A+B =170+C

A+B = 170+130-A ( c=130-A)

A+B = 300-A

2A+B = 300

A+B= 300/2

A+B = 150

A+B-C= 170

A+B = 170+C

150 = 170 +C ( A+B = 150)

or, C = 20..............................(1.)

A+C =130

or,A+ 20= 130 ( A=110).....................(2)

A+B = 150

110+B= 150

B = 150-110

B= 40..........................................(3)

Therefore, A = 110, B= 40, C=20..

MrRoyal

The solutions to the system of equations is A = 20, B = 150 and C = 0

The equations are given as:

[tex]A + B + C = 170[/tex]

[tex]B + C - A = 130[/tex]

Subtract the second equation from the first equation

[tex]A + B + C - (B + C - A )= 170 -130[/tex]

Open brackets

[tex]A + B + C - B - C + A = 170 -130[/tex]

[tex]A + B + C - B - C + A = 40[/tex]

Collect like terms

[tex]A + A + B - B + C - C = 40[/tex]

[tex]2A = 40[/tex]

Divide both sides by 2

[tex]A = 20[/tex]

Add both equations

[tex]A + B - C + (B + C - A) = 170 + 130[/tex]

Remove bracket

[tex]A + B - C + B + C - A = 170 + 130[/tex]

Collect like terms

[tex]A - A+ B + B - C + C = 170 + 130[/tex]

[tex]2B = 300[/tex]

Divide both sides by 2

[tex]B = 150[/tex]

Substitute 150 for B and 20 for A in [tex]A + B - C = 170[/tex]

[tex]20 + 150 - C = 170[/tex]

[tex]170 - C = 170[/tex]

Subtract 170 from both sides

[tex]C= 0[/tex]

Hence, the solutions to the system of equations is A = 20, B = 150 and C = 0

Read more about system of equations at:

https://brainly.com/question/14323743

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