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Q: What are linear equations with the same solutions called?

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You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.

The equations are equivalent.

No. A pair of linear equation can have 0 solutions (they are parallel), or one solution (they cross at one point) or an infinite number of solutions (they represent the same line).

A system of linear equations that has one unknown is a set of equations that all depend on the same variable. An example is y = 1 + 3x and y = 4 + 7x.

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A system of linear equations.

they have same slop.then two linear equations have infinite solutions

Two dependent linear equations are effectively the same equation - with their coefficients scaled up or down.

Simultaneous equations have the same solutions.

Simultaneous equations have the same solutions.

Equations with the same solution are called dependent equations, which are equations that represent the same line; therefore every point on the line of a dependent equation represents a solution. Since there is an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example, 2x + y = 8 4x + 2y = 16 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. A system of linear equations is consistent if there is only one solution for the system. A system of linear equations is inconsistent if it does not have any solutions.

If the equations are linear, they may have no common solutions, one common solutions, or infinitely many solutions. Graphically, in the simplest case you have two straight lines; these can be parallel, intersect in a same point, or actually be the same line. If the equations are non-linear, they may have any amount of solutions. For example, two different intersecting ellipses may intersect in up to four points.

It means that the equations are actually both the same one. When they're graphed, they both turn out to be the same line.

Simultaneous equations have the same solutions

A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.

Simultaneous equations have the same solutions.

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.

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