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### Differential Equations – Existence and Uniqueness Theorem

Differential Equations – Existence and Uniqueness Theorem

Differential Equations – Existence and Uniqueness Theorem

### y=x2−4x+4y=4−xIf the ordered pair (x,y) satisfies the system of equations.. ^{[1]}

If the ordered pair satisfies the system of equations above, what is one possible value of ?. Learn from their 1-to-1 discussion with Filo tutors.

In the figure above, what is the area of parallelogram ?. What is an integral solution to the equation above?

Kyle ate 20 percent more chicken wings and 40 percent more hot dogs. Considering only chicken wings and hot dogs, Kyle ate approximately percent more food, by weight, than John

### Solve Quadratic equations -y^2-4y-8=0 Tiger Algebra Solver ^{[2]}

Step-1 : Multiply the coefficient of the first term by the constant 1 • 8 = 8. Step-2 : Find two factors of 8 whose sum equals the coefficient of the middle term, which is 4 .

Our parabola opens down and accordingly has a highest point (AKA absolute maximum) . We know this even before plotting “t” because the coefficient of the first term, -1 , is negative (smaller than zero).

Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

### Which of the following equations have x =4 and y =2 as a solution?A. 2 x+3 y=12B. 4 x + y =19C. x+y=6D. 3 x+2 y=15 ^{[3]}

Which of the following equations have x=4 and y=2 as a solution?. Putting x=4 and y=2 in each of the given equations, we get the following:

### Question 17 How many linear equations in x and y can be satisfied by x = 1 and y = 2? A) Only one B) Two C) Infinitely many D) Three ^{[4]}

On putting x = 1 and y = 2, in above equation we get;. ⇒ a + 2b + c = 0, where a, b and c, are real number.

Hence, infinitely many linear equations in x and y can be satisfied by x = 1 and y = 2.

### The value of the variable which satisfies the equation is called of the equation. ^{[5]}

The value of the variable which satisfies the equation is called _________ of the equation.. The value of the variable in an equation which satisfies the equation is called a ___________ of the equation.

Complete the table by writing whether the given value of the variable satisfies the equation or not.. The value of a variable in a linear equation that satisfies the equation is called a _____ of an equation

### [Solved] Which of the following options is the solution of the given ^{[6]}

Which of the following options is the solution of the given equation:-. Note: For this type questions always refer the options first.

Now put the values from the given option simultaneously option (2) (5,-5). Now put the values from the given option simultaneously option (3) (6, -1)

RRB NTPC Result, Cut Off for Pay Level 5 declared for RRB Chandigarh. Earlier, the RRB had released the tentative schedule for the upcoming DV &Medical Examination for various posts.

### How do you solve this system of equations: #x- 4y \geq 4; 4y – x > 8#? ^{[7]}

How do you solve this system of equations: #x- 4y \geq 4; 4y – x > 8#?. The equations are inconsistent and there is no solution.

Because the slopes are the same, the lines are parallel.. That means that they will never have an intersection point, a point that satisfies both equations.

This is not true, so the equations are inconsistent.

### Pair of Linear Equations in Two Variables Class 10 Notes With Examples ^{[8]}

CBSE Class 10 Maths Chapter 3 Pair Of Linear Equations In Two Variables Notes. CBSE Class 10 Maths Chapter 3 Pairs of Linear Equations in Two Variables notes are available here

This chapter will help you to determine the values of the unknown variables with the help of various methods, such as the Graphical method and Algebraic methods. An example of pairs of linear equations will be: Rohan bought 2 pencils and 1 pen for Rs.10, whereas Sam bought 4 pencils and 2 pens for Rs

Hence, by solving the pair of linear equations in two variables, we will get the price of a pen and pencil. Let us go through the article to understand how to solve such a pair of equations.

### x = y – (50/y), where x and y are both > 0  ^{[9]}

|C) increase four fold||D) increase to more than double|. The best approach is to pick a number that satisfies the rules that x and y are greater than 0

The value after doubling y will be 50 – 50/50 = 49, which is more than double.

### Linear Systems with Two Variables and Their Solutions ^{[10]}

Real-world applications are often modeled using more than one variable and more than one equation. A system of equationsA set of two or more equations with the same variables

In this section, we will study linear systemsA set of two or more linear equations with the same variables. consisting of two linear equations each with two variables

To check that an ordered pair is a solution, substitute the corresponding x- and y-values into each equation and then simplify to see if you obtain a true statement for both equations.. Determine whether or not (1, 0) is a solution to the system .

### $\sqrt{y + 1} – \sqrt{y – 1} = \sqrt{4y – 1}$. Find the value of $y$. ^{[11]}

Consider function on LHS, $\sqrt{y+1} – \sqrt{y-1}$. It is not defined for $y

At $y=1$, RHS is $\sqrt3$, which is greater than the maximum value of LHS.. Coming back to your question, it is important to note that when you square an equation, it can introduce additional roots

$1-2y=2\sqrt{(y+1)(y-1)}$which renders as $1-2y=2\sqrt{(y+1)(y-1)}$

### Illustrative Mathematics ^{[12]}

If possible, find a second linear equation to create a system of equations that has:. Bonus Question: In each case, how many such equations can you find?

To have exactly one solution, we want the graph of $5x – 2y = 3$ and the graph of the equation we come up with to intersect at exactly one point, as shown below.. To do this, we find a point on the line $5x – 2y = 3$ and create another line that also contains that point but is not the same line

By substitution, we see that\begin{align} 5(3) – 2y &= 3 \implies \\ 15 – 2y &= 3 \implies\\ y &= 6 \end{align}. Now we find any values $a$,$b$, or $c$ in the equation $ax+by=c$ that “work” with $x = 3$ and $y = 6$ and are not the same values as in the given equation

### Sources

- https://askfilo.com/mathematics-question-answers/yx2-4-x4y4-xif-the-ordered-pair-x-y-satisfies-the-system-of-equations-above-what-351247
- https://www.tiger-algebra.com/drill/-y~2-4y-8=0/
- https://byjus.com/question-answer/which-of-the-following-equations-have-x-4-text-and-y-2-as-a-solution-1/#:~:text=Hence%2C%20x%3D4%2Cy,equation%20x%2By%3D6.
- https://byjus.com/question-answer/how-many-linear-equations-in-x-and-y-can-be-satisfied-by-x-1-1/#:~:text=Hence%2C%20infinitely%20many%20linear%20equations,%3D%201%20and%20y%20%3D%202.
- https://byjus.com/question-answer/the-value-of-the-variable-which-satisfies-the-equation-is-called-of-the-equation/#:~:text=A%20the%20solution-,The%20value%20of%20the%20variable%20which%20satisfies%20the%20equation,the%20solution%20of%20the%20equation.
- https://testbook.com/question-answer/which-of-the-following-options-is-the-solution-of–600babcaf88c98989c148584
- https://socratic.org/questions/how-do-you-solve-this-system-of-equations-x-4y-geq-4-4y-x-8
- https://byjus.com/cbse-notes/cbse-class-10-maths-notes-chapter-3-pair-of-linear-equations-in-two-variables/
- https://www.sawaal.com/numbers-questions-and-answers/x-y-50-y-where-x-and-y-are-both-gt-0-nbsp–if-the-value-of-y-is-doubled-in-the-equation-above-the-_4487
- https://saylordotorg.github.io/text_intermediate-algebra/s06-01-linear-systems-with-two-variab.html
- https://math.stackexchange.com/questions/4704980/sqrty-1-sqrty-1-sqrt4y-1-find-the-value-of-y
- https://tasks.illustrativemathematics.org/content-standards/tasks/554