What is the answer for this using substitution?
1 answer:
9514 1404 393
Answer:
(x, y) = (2, -2)
Step-by-step explanation:
We would normally choose to use substitution when x or y could be easily solved-for without having fractions involved. That is not the case here. However, we observe that the term 3y appears in both equations, so we can substitute for "3y" instead of "y".
From the second equation, ...
3y = 5x -16
Substituting into the first equation, ...
2x +(5x -16) = -2
7x = 14 . . . . . . . . . add 16
x = 2 . . . . . . . . . . divide by 7
Using our equation for y, we get ...
3y = 5(2) -16 = -6
y = -2 . . . . . . . . . divide by 3
The solution is (x, y) = (2, -2).
You might be interested in
Answer:
The measure of anle MNP is
- m ∠ MNP = (x - y)/2
Explanation:
The image attached shows the figure corresponding to this question.
The <em>angle MNP</em>, wich is also the angle LNP, is formed by the intersection of a secant and a tanget to a circle.
Then, you can use the theorem:
- the angle formed by a secant and a tangent to a circle that intersect outside the circle is half the difference of the major arc minus the minor arc.
The major arc formed is identified with the letter x and the minor arc is identified witht he letter y. Thus, the measure of the angle MNP is half the differenc x - y:
- m ∠ MNP = (x - y)/2
Answer:
The following measurements are:
(Option #4)
(Option #7)
(Option #5)
(Option #2)
Step-by-step explanation:
To begin, we can find the measure of by applying the inscribed angle theorem: an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.
Since the intercepted arc (RS) is 46 degrees, we have:
Next, we can find the measure of arc QT using the same theorem. So,
Notice that the chord RT is actually a diameter. From the theorem about the inscribed angle including a diameter, we know that the intercepted arc will have a measure of . Since the arc ST is part of the arc RST, and we know RS is
, we can set up and solve this equation:
We can use the same idea to find RQ. We know that RQT is and QT is
, so: