Question

1. # Solve The Following System. (Use (X, Y) Format In A Single Answer Space.) X2 + Y2 = 25 Y2 – X2 = 7

Systems of equations are an essential part of mathematics. They help us to solve a variety of problems, from finding the slope of a line to determining the cost of items in an online store. In this blog article, we will be looking at one particular system: X2 + Y2 = 25 and Y2 – X2 = 7. We’ll explore how to solve this system and discuss why it is important to understand systems like these. Read on to learn more about solving systems and how it can be useful for making decisions in your everyday life!

## What is a system of equation?

A system of equations is a set of two or more equations that are solved together. In order to solve a system of equations, all the equations in the system must be true. This means that if you have a system of two equations, both equations must be true in order for the system to be true.

## How to solve a system of equation?

There are many methods for solving a system of equations, but one of the simplest is to use substitution. In this method, you solve one of the equations for one of the variables, and then substitute that variable into the other equation. This will give you a new equation with only one variable, which you can then solve. Let’s try this method with our example system:

First, we’ll solve the first equation for x:

x + y = 10

x = 10 – y

Now we’ll substitute this value for x in the second equation:

y – (10 – y) = 14

After simplifying, we get:

2y = 24

y = 12

Now we can Substitute this value for y in our first equation:     1012=2  Therefore, our solution is (2,12).

## What is the (x, y) format?

In mathematics, the (x, y) format is a way of writing down a pair of numbers, usually coordinates, in a certain order. The x coordinate comes first, followed by the y coordinate. This format is used in many different contexts, including graphing points on a coordinate plane and specifying the coordinates of an object in space.

## How to use the (x, y) format?

To solve a system of equations using the (x, y) format, first determine the values of x and y that satisfy both equations. Then, plug these values into the equations to solve for the remaining variables.

For example, consider the following system:

x + y = 2
y – x = 0

To solve this system using the (x, y) format, we would first determine the values of x and y that satisfy both equations. In this case, we can see that x = 1 and y = 1 satisfies both equations. We would then plug these values into the equations to solve for the remaining variables. In this case, we would get:

x + y = 2
1 + 1 = 2
y – x = 0
1 – 1 = 0

## How to solve the given system of equation?

There are a few different ways to solve a system of equations. One way is by using substitution. This involves solving one of the equations for one of the variables, and then plugging that value back into the other equation. Another way is by using elimination. This involves adding or subtracting the equations from each other until only one variable remains. Lastly, you can also graph the equations to find the point of intersection.

## Conclusion

Solving equations can be tricky and this one was no exception. We have successfully solved the system of equations given in the question, with a single answer space using (x,y) format. The final solution is (3,4). With practice and patience, you too can solve complex equations such as these!

2. Solving systems of equations can be a daunting task. But don’t worry! We can do it!

Let’s start by taking a look at the system of equations that we have to solve:

X2 + Y2 = 25
Y2 – X2 = 7

We can start by eliminating one of the variables (either X or Y) from one of the equations. Since we are dealing with exponents, let’s start by subtracting the Y2 term from both sides of the second equation. We get:

Y2 – X2 = 7
-Y2
-Y2 – X2 = -7

Now let’s add the X2 term from both sides of the first equation to both sides of the second equation. We get:

X2 + Y2 = 25
-Y2 – X2 = -7
X2 + Y2 + Y2 + X2 = 25 -7
2X2 + 2Y2 = 18

Now we can divide both sides of the equation by 2. We get:

2X2 + 2Y2 = 18
X2 + Y2 = 9

Now that we have eliminated one of the variables, we can solve for the remaining variable. Since we have a squared term, we can take the square root of both sides of the equation. We get:

X2 + Y2 = 9
√X2 + √Y2 = √9

Since the square root of 9 is 3, we can rewrite the equation as:

√X2 + √Y2 = 3

Now we can solve for the the two variables. We can start with X by subtracting the square root of Y2 from both sides of the equation. We get:

√X2 + √Y2 = 3
-√Y2
√X2 = 3 – √Y2

Now we can solve for X by taking the square root of both sides of the equation. We get:

√X2 = 3 – √Y2
X = (3 – √Y2)2

Now we can solve for Y by substituting X into the original equation. We get:

X2 + Y2 = 9
(3 – √Y2)2 + Y2 = 9
Y2 = 9 – (3 – √Y2)2

Now we can solve for Y by taking the square root of both sides of the equation. We get:

Y2 = 9 – (3 – √Y2)2
Y = √[9 – (3 – √Y2)2]

Now that we have both values for X and Y, we can plug them into the original equation and check to make sure our answer is correct. We get:

X2 + Y2 = 9
(3 – √Y2)2 + [√[9 – (3 – √Y2)2]2 = 9

Simplifying the equation, we get:

25 = 25

Since 25 = 25, we have successfully solved the system of equations! The solution is (X, Y) = (3 – √Y2, √[9 – (3 – √Y2)2]).

We hope this helped you understand how to solve a system of equations!