Solve the linear system of equations using the linear combination method
4x +5y=7
y=3x+9
enter your answers in the boxes.
x=
y=

x = -2

y = 3

Step-by-step explanation:

Write the system the following way:

4x + 5y = 7

-3x +y  = 9

we need to eliminate one unknown by multiplying one equation for a suitable number in such a way that when we add the equations one unknown is eliminated.

If we multiply the second eq. by -5 the y is eliminated

4x + 5y = 7

15x -5y = -45

add the equations

19x = -38 ===> x = -38/19 ===> x = -2

Now replace this value in any equation to get y. For example, in 1st one.

4(-2) + 5y = 7 ===> -8 +5y = 7 ===> 5y = 7+8 ===> 5y = 15 ===> y = 15/5 ===>

y=3

.

step-by-step explanation:

∠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.