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What is the best method for solving a set of two linear equations?
If this involves two equations both containing the same two unknowns, then multiply (or divide) one of the equations so that the absolute value of one of the unknowns is now the same in both equations. For example, x + 2y = 11 : 3x - 57 = 13 : Multiply the first equation by three, 3x + 6y = 33 so that the 'x' terms in this and the second equations are equal. In this example they both have the same (positive) sign - see below.If this unknown has identical signs (both are positive or both are negative) then subtract one equation from the other to eliminate that unknown.If this unknown has different signs (it is positive in one equation and negative in the other equation) then add the equations together to eliminate that unknown.This will enable the value of the remaining unknown to be determined and by substitution the value of the eliminated unknown can then be found.
What does it mean if there are an infinite number of solutions for a system of linear equations?
It means that the equations are actually both the same one. When they're graphed, they both turn out to be the same line.
Why is function and linear equation difference?
Functions and linear equations are the same in that they both deal with x and y coordinates and points on a graph but have differences in limitations, appearance and purpose. Often, functions give you the value of either x or y, but linear equations ask to solve for both x and y.
What is algebraic strategy for solving a system of equations when two expressions are the same?
An expression is the algebraic representation of a number - an expression has a numeric value.An equation is an algebraic statement claiming that two expressions have the same numeric value. The equation has a Boolean value (true or false).If two equations can be expressed in an identical manner (the same expression on both sides) - then these equations are the same equation.In order for a system of equations to have a solution, the number of different equations in the system must be equal to the number of variables in the system. If there are more distinct equations than there are variables, than the system has no solution. If there are less, then the system may have no solution, or infinitely many solutions.In the case described there is most likely an infinite number of solutions
What is the basic rules to solve equations?
The basic rules to solve equations are to isolate the variable on one side of the equation by performing the same operation on both sides. This includes adding or subtracting the same value, multiplying or dividing by the same value, and applying exponent or logarithm rules if necessary. The goal is to simplify the equation until the variable is alone on one side and the solution can be determined.
Expressions that have the same value?
If both equations can be simplified to the same value, they are equal.
What is the best method for solving a set of two linear equations?
If this involves two equations both containing the same two unknowns, then multiply (or divide) one of the equations so that the absolute value of one of the unknowns is now the same in both equations. For example, x + 2y = 11 : 3x - 57 = 13 : Multiply the first equation by three, 3x + 6y = 33 so that the 'x' terms in this and the second equations are equal. In this example they both have the same (positive) sign - see below.If this unknown has identical signs (both are positive or both are negative) then subtract one equation from the other to eliminate that unknown.If this unknown has different signs (it is positive in one equation and negative in the other equation) then add the equations together to eliminate that unknown.This will enable the value of the remaining unknown to be determined and by substitution the value of the eliminated unknown can then be found.
What is the same about expressions and equations?
They both have numbers and symbols
What does it mean if there are an infinite number of solutions for a system of linear equations?
It means that the equations are actually both the same one. When they're graphed, they both turn out to be the same line.
What does it mean both algebraically and graphically when an ordered pair is a solution to a system of two linear equations?
If an ordered pair is a solution to a system of linear equations, then algebraically it returns the same values when substituted appropriately into the x and y variables in each equation. For a very basic example: (0,0) satisfies the linear system of equations given by y=x and y=-2x By substituting in x=0 into both equations, the following is obtained: y=(0) and y=-2(0)=0 x=0 returns y=0 for both equations, which satisfies the ordered pair (0,0). This means that if an ordered pair is a solution to a system of equations, the x of that ordered pair returns the same y for all equations in the system. Graphically, this means that all equations in the system intersect at that point. This makes sense because an x value returns the same y value at that ordered pair, meaning all equations would have the same value at the x-coordinate of the ordered pair. The ordered pair specifies an intersection point of the equations.
How can you tell linear equations are parallel?
Equations are never parallel, but their graphs may be. -- Write both equations in "standard" form [ y = mx + b ] -- The graphs of the two equations are parallel if 'm' is the same number in both of them.
Can you solve system of equations by graphing?
Yes you can, if the solution or solutions is/are real. -- Draw the graphs of both equations on the same coordinate space on the same piece of graph paper. -- Any point that's on both graphs, i.e. where they cross, is a solution of the system of equations. -- If both equations are linear, then there can't be more than one such point.
Are 4y-3x equals 1 and 2y equals 3 over 2x -14 perpendicular or parallel?
They are parallel because the slope has the same value in both equations.
Is ionic equation and balanced equation are the same equations?
No, but both describe the same chemical reaction.
Why is function and linear equation difference?
Functions and linear equations are the same in that they both deal with x and y coordinates and points on a graph but have differences in limitations, appearance and purpose. Often, functions give you the value of either x or y, but linear equations ask to solve for both x and y.
What is algebraic strategy for solving a system of equations when two expressions are the same?
An expression is the algebraic representation of a number - an expression has a numeric value.An equation is an algebraic statement claiming that two expressions have the same numeric value. The equation has a Boolean value (true or false).If two equations can be expressed in an identical manner (the same expression on both sides) - then these equations are the same equation.In order for a system of equations to have a solution, the number of different equations in the system must be equal to the number of variables in the system. If there are more distinct equations than there are variables, than the system has no solution. If there are less, then the system may have no solution, or infinitely many solutions.In the case described there is most likely an infinite number of solutions
How are the rules for solving inequalities similar to those for solving equations?
Solving inequalities and equations are the same because both have variables in the equation.
