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.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

9987

step-by-step explanation: