Across
3. An equation of the form ax + by +c =0 where a,b,c are real and a,b cannot be zero simultaneously and x,y are variables , is
called a --------------- equation in two variables x,y.
4. Value of the variable x which when substituted in the equation , makes two sides of the equation equal, is called ---------------
of the equation.
5. First natural number is -------------(in words).
6. Every linear equation in two variables has an ------------- number of solutions.
Down
1. A symbol which takes various numerical values is known as a -------------------
2. Addition of one with one gives -------------.
19. Solve the following linear equation:
(3−2)
4
-
(2+3)
3
=
2
3
- t
20. The dimensions of a cuboid are in the ratio 2: 3 :4 and its total surface area is 5200 cm2
. Find the volume of the cuboid
Answers
Step-by-step explanation:
Across
3. An equation of the form ax + by +c =0 where a,b,c are real and a,b cannot be zero simultaneously and x,y are variables , is
called a --------------- equation in two variables x,y.
4. Value of the variable x which when substituted in the equation , makes two sides of the equation equal, is called ---------------
of the equation.
5. First natural number is -------------(in words).
6. Every linear equation in two variables has an ------------- number of solutions.
Down
1. A symbol which takes various numerical values is known as a -------------------
2. Addition of one with one gives -------------.
19. Solve the following linear equation:
(3−2)
4
-
(2+3)
3
=
2
3
- t
20. The dimensions of a cuboid are in the ratio 2: 3 :4 and its total surface area is 5200 cm2
. Find the volume of the cuboid
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Answer:
An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in two variables. Here a and b are called coefficients of x and y respectively and c is called constant term.
Step-by-step explanation:
In mathematics, a linear equation is an equation that may be put in the form
{\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}+b=0,}{\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}+b=0,}
where {\displaystyle x_{1},\ldots ,x_{n}}x_{1},\ldots ,x_{n} are the variables (or unknowns), and {\displaystyle b,a_{1},\ldots ,a_{n}}{\displaystyle b,a_{1},\ldots ,a_{n}} are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients {\displaystyle a_{1},\ldots ,a_{n}}a_1, \ldots, a_n are required to not all be zero.
Alternatively a linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken.
The solutions of such an equation are the values that, when substituted for the unknowns, make the equality true.
In the case of just one variable, there is exactly one solution (provided that {\displaystyle a_{1}\neq 0}{\displaystyle a_{1}\neq 0}). Often, the term linear equation refers implicitly to this particular case, in which the variable is sensibly called the unknown.
In the case of two variables, each solution may be interpreted as the Cartesian coordinates of a point of the Euclidean plane. The solutions of a linear equation form a line in the Euclidean plane, and, conversely, every line can be viewed as the set of all solutions of a linear equation in two variables. This is the origin of the term linear for describing this type of equations. More generally, the solutions of a linear equation in n variables form a hyperplane (a subspace of dimension n − 1) in the Euclidean space of dimension n.
Linear equations occur frequently in all mathematics and their applications in physics and engineering, partly because non-linear systems are often well approximated by linear equations.