Question

solve the equation by Cramer's rule; x+y=3; y+z=5; z+x=4​

Answer 1

Answer:

z=3,y=2,x=1

Step-by-step explanation:

y+z-x-y=5-3

=z-x=2

z-x+z+x=4+2

=2z=6

=z=3

3+x=4

=x=1

1+y=3

=y=2

Answer 2

Answer:

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

Step-by-step explanation:

According to Linear Algebra, cramer’s rule is defined as the method in which the values of any variables in the system are there it will be calculated by using the matrices of the determinants.

Types of matrices in cramer’s rule:

1) 2X2 Matrices rule

2) 3X3 Matrices Rule

Conditions to be followed for cramer’s rule:

1) The Cramer’s rule will fail only when the system of the equations in which D = 0.

2)It is due to the reason that, when we find the values of the unknown. The D must be visible in the denominator and the values will turn out to be undefined.

3) Let us understand that, when D=0, there will be no solutions for the systems.

Given that:

x+y=3; y+z=5; z+x=4

To find:

The Cramer’s rule for the Equation=?

Solution:

Let us consider that, by equation all the values,

We get,

X+y =3, y+z= 5

We get,

y+z-x-y=5-3

=z-x=2

Now, again let us consider that,

Y+z=5, z+x=4

We get,

z-x+z+x=4+2

=2z=6

z=3

putting the values of z in equation z+x=4,

we get,

3+x=4

x=1

now, again putting the value of x in the equation, x+y=3,

we get,

1+y=3

y=2

Therefore, the values are x =1 , y =2 and z =3.

#SPJ3