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How do you know that substitution gives the answer to a system of equations?
Wiki User
∙ 10y ago
You put in the answers you got for your variables into one of the equations. If it gives you the correct answer then you solved it, if it's different then either it doesn't work or one of the steps wasn't completed correctly or at all.
Wiki User
∙ 10y ago
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How do you know if a point is a solution to a system of equations?
The coordinates of the point satisfy each of the equations.
How would you know if a linear system has a solution?
One way is to look at the graphs of these equations. If they intersect, the point of intersection (x, y) is the only solution of the system. In this case we say that the system is consistent. If their graphs do not intersect, then the system has no solution. In this case we say that the system is inconsistent. If the graph of the equations is the same line, the system has infinitely simultaneous solutions. We can use several methods in order to solve the system algebraically. In the case where the equations of the system are dependent (the coefficients of the same variable are multiple of each other), the system has infinite number of solutions solution. For example, 2x + 3y = 6 4y + 6y = 12 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. Try to solve this system of equations, 2x + 3y = 6 4x + 6y = 7 If you use addition or subtraction method, and you obtain a peculiar result such that 0 = 5, actually you have shown that the system has no solution (there is no point that satisfying both equations). When you use the substitution method and you obtain a result such that 5 = 5, this result indicates no solution for the system.
How do you know when an algebraic equation has infinitely many solutions?
A system of equations has an infinite set of solutions when the equations define the same line, such that for ax + by = c, the values for two equations is a1/a2 + b1/b2 = c1/c2. Equations where a variable drops out completely, e.g. 3x - y = 6x -2y there are either an infinite number of solutions, or no solution at all.
What is a linear system?
A linear system is an equation to find the intersection of two or more lines. The equations are usually expressed with two variables, x and y. I don't know yet, but maybe geometry might have three variables, including z. Basically it's where two lines intersect and the most common ways of solving it are through graphing, substitution, and/or elimination.Presume you mean "linear".These are systems whose parameters vary directly or proportionally. Plotting functions results in straight lines.
Is linear algebra and linear equations the same?
Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a point where they all intersected, you would use Linear Algebra to solve that question. Linear Algebra uses matrices to solve these large systems of equations.
How do you know if a point is a solution to a system of equations?
The coordinates of the point satisfy each of the equations.
How do you know that solutions using substitution gives the answer ot the system of equations?
Here's a mark you use in your math every day, and right now, you have to stopfor a second and understand and accept what it really means:=See that ? That's the "equals" sign. When you write (one quantity) = (another quantity), that means that honestly and truly, those two quantities are not only 'equivalent', butliterally equal in every way. Either one can do anything and everything that the otherone can do, and wherever you see one of them, you can stick the other one in its place,because they're equal in every way.That's why substitution is a legitimate operation. If a statement is true before substitution,it's still true after substitution.
How would you know if a linear system has a solution?
One way is to look at the graphs of these equations. If they intersect, the point of intersection (x, y) is the only solution of the system. In this case we say that the system is consistent. If their graphs do not intersect, then the system has no solution. In this case we say that the system is inconsistent. If the graph of the equations is the same line, the system has infinitely simultaneous solutions. We can use several methods in order to solve the system algebraically. In the case where the equations of the system are dependent (the coefficients of the same variable are multiple of each other), the system has infinite number of solutions solution. For example, 2x + 3y = 6 4y + 6y = 12 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. Try to solve this system of equations, 2x + 3y = 6 4x + 6y = 7 If you use addition or subtraction method, and you obtain a peculiar result such that 0 = 5, actually you have shown that the system has no solution (there is no point that satisfying both equations). When you use the substitution method and you obtain a result such that 5 = 5, this result indicates no solution for the system.
How do you solve a system of equation with 3 equations and 3 variables?
If you know matrix algebra, the process is simply to find the inverse for the matrix of coefficients and apply that to the vector of answers. If you don't: You solve these in the same way as you would solve a pair of simultaneous linear equations in two unknowns - either by substitution or elimination. For example, change the subject of one of the equations to express one of the variables in terms of the other two. Substitute this value into the other two equations. When simplified, you will have two linear equations in two variables.
How do you know if a system has one solution?
If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.
Use the substitution method to solve the system of equations. Choose the correct ordered pair. 2y plus 2x 20 y - 2x 4?
It is not possible to know exactly what the question is because the browser used by this site is almost totally useless for mathematical questions: it rejects most symbols. If the equations are 2y + 2x = 20 and y - 2x = 4,then the solution is (2, 8).
What is a mutation you might have but not know about?
substitution
Explain why a system of linear equations cannot have exactly two solutions?
if you can fart out of your chin then you know your headin in the right direction
How do you solve a system of linear equations by graphing?
When you are solving a system of linear equations, you are looking for the values for the unknown variables (usually named x and y) that make each equation in the system true. Instead of using algebraic substitution or elimination, you can use graphing to find the variables. If you graph each equation on the same graph, the point where the graphs cross is the answer, which should be given as an ordered pair in the form (x,y). If the graphs do not cross anywhere (for example, parallel lines) then there is no solution. If the graphs of two lines end up being the same line, then there are an infinite number of solutions. You must know how to graph a line in order to use this method.
Where do you use formulating equations in life?
well, if you know all the formulating equations it will make you better at regular equations and regular equations can be used in everyday life
How do you know when an algebraic equation has infinitely many solutions?
A system of equations has an infinite set of solutions when the equations define the same line, such that for ax + by = c, the values for two equations is a1/a2 + b1/b2 = c1/c2. Equations where a variable drops out completely, e.g. 3x - y = 6x -2y there are either an infinite number of solutions, or no solution at all.
How do you do linear equations?
To solve linear equations, you always use the inverse operations
