Solve the system of equations by elimination.
2x - y + 3z=-1
x + 2y - 4z=-1
y – 2z=0

x = -1, y = 2 and z = 1

Step-by-step explanation:

The given system of equations are :

2x - y + 3z= -1  (1)

x + 2y - 4z = -1  (2)

y – 2z = 0  (3)

Equation (3) can be written as :

y = 2z

Use y = 2z in equation (2)

x + 2(2z) - 4z = -1

x + 4z - 4z = -1

x = -1

Put the value of x in equation (1) :

-2 -y +3z = -1

-y+3z = 1 (4)

Adding equation (3) and (4)

y-2z+(-y+3z)=1

z = 1

Now put z = 1 in equation (4)

-y+3=1

-y = -2

y = 2

Hence, the values of x,y and z are -1, 2 and 1 respectively.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions