Solve the following system of equations graphically.
y = 2x - 3
x + y = 3
what is the solution set?
{(2, 1)}
{(1, 2)}
{(-1, -2)}
{(-2, -1)}

(2,1)

Step-by-step explanation:

Let us graph our first equation

y = 2x - 3

Bring y to the right hands side and 3 to the left hand side of = we get

2x-y=3

Diving each term of the equation by 3 we get

Hence we have converted our equation into intercept form, in x intercept is and y intercept is -3.

Now we mark the two points are as and (0,-3)

Shown as red line in attachment.

x + y = 3

Dividing both sides by 3

Hence our x and y intercepts are 3. Thus we plot coordinates (3,0) and (0,3) and join them together to graph our line.In attachment it is shown in as blue line.

Please refer to the image in the attachment. The two lines intersect at (2,1)

This is our solution.

∠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.

step-by-step explanation: