Question

The following equations are given

Answer 1

The required values are x = 2, y = -1 and z = 3

What are system of equations?

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equation for which common solutions are sought.

The given set of equations are :

Equation #1 3x+z+y=8

Equation #2 5y-x=-7

Equation #3 3z+2x-2y=15

Equation #4 4x+5y-2z=-3

a. It is not possible  to solve for any of the variables using only Equation #1 and Equation #2

As there are 3 variables x,y and z in the given system of equations so we need 3 equations.

If we take only Equation #1 and Equation #2 , Equation #1 contains 3 variables and Equation #2 contains only 2 variable.

b. it is possible to solve for any of the variables using only Equation #1, Equation #2, and Equation #3

As there are 3 variables x,y and z in the given system of equations so we need 3 equations.

So, taking Equation #1, Equation #2, and Equation #3

Equation #1 3x+z+y=8

Equation #2 5y-x=-7

Equation #3 3z+2x-2y=15

From, Equation #1  we have

z =8 - 3x - y

Put this in Equation #3 we get,

7x +5y = 9

Solving  Equation #1, Equation #2 we get,

x = 2, and

y = -1

Again put the values of x and y in Equation #1 we get,

z = 3

Hence , the required values are x = 2, y = -1 and z = 3

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