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equivalent equations
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The solution to a two-variable system is the point on a graph at which the lines cross?
Yes, the solution to a two-variable system is the point where the equations of the lines representing the system intersect on a graph. This point represents the values of the variables that satisfy both equations simultaneously.
What does equations mean?
Equations are mathematical statements that show the equality of two expressions, typically separated by an equal sign. They are used to solve for unknown variables by manipulating the expressions to find a solution that satisfies the equation. Equations play a fundamental role in mathematics and are used in various fields to describe relationships between quantities.
What is a solution of two or more solids called?
If the two solids are both metals, then the result is an alloy. However, cast iron for example is a mixture of carbon and iron, so technically it may be an alloy. But a car tyre is made of rubber, chalk, sulphur, rosin, etc. I guess the only answer for this is a mixture. If the two metals are in fluid solution, then it is a mixture.
The concentration of a solution of two or more liquids is expressed as a percentage by?
The concentration of a solution of two or more liquids is expressed as a percentage by dividing the amount of solute by the total amount of solution (solute + solvent) and multiplying by 100.
What is meant by solution?
A solution refers to a homogeneous mixture composed of two or more substances. In a solution, the solute is dissolved in the solvent, resulting in a single phase with uniform composition. Solutions can be in various states, such as solid, liquid, or gas.
What is the consistent equation in mathematics?
Consistent equations are two or more equations that have the same solution.
What are two equations that have the same solution?
equal equations.
What are equations with same solution called?
There is no special name. Two totally unrelated equations could have the same solution(s).
A definition of a solution to a system of equations?
A system of equations is a set of two or more equations with the same variables, graphed in the same coordinate plane
How can you tell that an equation has the same solution as the original equation?
If the two equations are linear transformations of one another they have the same solution.
Does every pair of linear simultaneous equations have a solution?
Actually not. Two linear equations have either one solution, no solution, or many solutions, all depends on the slope of the equations and their intercepts. If the two lines have different slopes, then there will be only one solution. If they have the same slope and the same intercept, then these two lines are dependent and there will be many solutions (infinite solutions). When the lines have the same slope but they have different intercept, then there will be no point of intersection and hence, they do not have a solution.
How could you show that two equations aren't equivalent?
One way would be to solve the two equations. If they have exactly the same solution set, they are equivalent. Otherwise they are not.
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
Do equations with different slopes and different y-intercepts have a solution?
TWO linear equations with different slopes intersect in one point, regardlessof their y-intercepts. That point is the solution of the pair.However, this does not mean that three (or more) equations in two variables, even if they meet the above conditions, have a solution.
What are two or more linear equations using the same variables called?
A system of linear equations.
Does every pair of linear simultaneous equations have a unique solution?
So, take the case of two parallel lines, there is no solution at all. Now look at two equations that represent the same line, they have an infinite number of solutions. The solution is unique if and only if there is a single point of intersection. That point is the solution.
What is the solution of a system of linear equations in two variables?
The solution of a system of linear equations is a pair of values that make both of the equations true.
