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if we take the (x1,y1),(x2,y2) as coordinates the formula was (x-x1)/(x2-x1)=(y-y1)/(y2-y1)

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What it means to be a solution to a linear system algebraically?

A linear system just means it's a line. A solution is just a point that is on that line. It means that the two coordinates of the point solve the equation that makes the line. Alternatively, it could mean there are 2 (or more) lines and the point is where they intersect; meaning its coordinates solve both (or all) equations that make the lines.


Why could a system of linear equations have two solutions?

A system of linear equations cannot have two distinct solutions if it is consistent and defined in a Euclidean space. If two linear equations intersect at a single point, they have one solution; if they are parallel, they have no solutions. However, if the equations are dependent, meaning one equation is a multiple of the other, they represent the same line and thus have infinitely many solutions, not just two. Therefore, in standard scenarios, a system of linear equations can either have one solution, no solutions, or infinitely many solutions, but not exactly two.


How does the bisection method work when solving nonlinear equations?

it works exactly the same as it does with linear equations, you don't need to do any differentiation or anything fancy with this method, just have to plug in values of x, so it shouldn't make a difference if the equation is linear or nonlinear.


When will be the linear equations a1x plus b1y plus c1 equals 0 and a2x plus b2y plus c2 equals 0 has unique solution?

When (the graph of the equations) the two lines intersect. The equations will tell you what the slopes of the lines are, just look at them. If they are different, then the equations have a unique solution..


What is subsituton method?

Its a method used to find out the common solution of a pair of linear equations in two variables. For it, just make the coefficients of any one term and if the coefficients are having same signs, subtract both and if they are having different signs, add them up.

Related Questions

What it means to be a solution to a linear system algebraically?

A linear system just means it's a line. A solution is just a point that is on that line. It means that the two coordinates of the point solve the equation that makes the line. Alternatively, it could mean there are 2 (or more) lines and the point is where they intersect; meaning its coordinates solve both (or all) equations that make the lines.


Why could a system of linear equations have two solutions?

A system of linear equations cannot have two distinct solutions if it is consistent and defined in a Euclidean space. If two linear equations intersect at a single point, they have one solution; if they are parallel, they have no solutions. However, if the equations are dependent, meaning one equation is a multiple of the other, they represent the same line and thus have infinitely many solutions, not just two. Therefore, in standard scenarios, a system of linear equations can either have one solution, no solutions, or infinitely many solutions, but not exactly two.


Why should you clear decimals when solving linear equations and inequalities?

It makes it allot less confusing. But, that is just my opinion.


How were linear equations invented?

carlos bert canospien is the inventer. he lives in 1860s. and i guess it just poped into his mind


How does the bisection method work when solving nonlinear equations?

it works exactly the same as it does with linear equations, you don't need to do any differentiation or anything fancy with this method, just have to plug in values of x, so it shouldn't make a difference if the equation is linear or nonlinear.


What are the coordinates for linear equation y2x and x y12?

y2x - just double the coordinate of y to get x. xy12 - i have no idea


How do you solve imaginary equations?

The answer depends on the nature of the equation. Just as there are different ways of solving a linear equation with a real solution and a quadratic equation with real solutions, and other kinds of equations, there are different methods for solving different kinds of imaginary equations.


When will be the linear equations a1x plus b1y plus c1 equals 0 and a2x plus b2y plus c2 equals 0 has unique solution?

When (the graph of the equations) the two lines intersect. The equations will tell you what the slopes of the lines are, just look at them. If they are different, then the equations have a unique solution..


Why do you clear decimals when solving linear equations and inequalities and example?

Even if you keep the decimal, later on you will still have to remove it. It is just an easier way to solve the equation.


What is subsituton method?

Its a method used to find out the common solution of a pair of linear equations in two variables. For it, just make the coefficients of any one term and if the coefficients are having same signs, subtract both and if they are having different signs, add them up.


Does linear mean straight?

Yes, the term "linear" typically refers to something that is straight or follows a straight line. In mathematics and geometry, linear relationships or equations represent a direct proportionality between variables, resulting in a straight line when graphed. However, "linear" can also refer to processes or patterns that are sequential or one-dimensional, not just in a geometric sense.


How do you solve linear equations with a fractions G - plus 2 equals 8 3?

one way is you could get rid of the fraction by the multiplying everything denominator of the fraction and then just solving it regularly.