The required values are x = 2, y = -1 and z = 3
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
More about system of equations :
https://brainly.com/question/2273153
#SPJ2
