Two Linear Equations With Infinite Solutions

On solving we have 7x 35 or x 5.

Two linear equations with infinite solutions. Since we divide both side of the equation by 3 the system of equation is said to have infinite solution if both the equations represents the same. Stack exchange network stack exchange network consists of 176 q a communities including stack overflow the largest most trusted online community for developers to learn share their knowledge and build their careers. If we multiply 5 to equation 1 we will achieve equation 2 and on dividing equation 2 with 5 we will get the exact first equation. Thus suppose we have two equations in two variables as follows.

A 1 x b 1 y c 1 1 a 2 x b 2 y c 2 2 the given equations are consistent and dependent and have. Y x 3 5y 5x 15. The above linear equation is only true if x 5 and hence the given linear equation has only one solution i e. Collect the like terms on both sides by transferring them we have.

Muriel says she has written a system of two linear equations that has an infinite number of solutions. B an infinite number of solutions. Can someone help me determine the value of a such that there are infinite many solutions for the given equation. If a pair of the linear equations have unique or infinite solutions then the system of equation is said to be a consistent pair of linear equations.

Hence a system will be consistent if the system of equations has an infinite number of solutions. This equation could also be written as. If the two equations are in standard form both variables on one side and a constant on the other side then the following are true. A only one solution 5 1.

Write a system of two linear equations that has. For example consider the following equations. Consider the equation 9 x 1 35 8x 37. On solving we have 9x 9 35 8x 37.

The first equation is given as. Consider the equation 7x 35 0. But in case of the two variable linear equation the solutions are calculated as the cartesian coordinates of a point of the euclidean plane. For a system of two linear equations and two variables there can be no solution exactly one solution or infinitely many solutions just like for one linear equation in one variable.

Although systems of linear equations can have 3 or more equations we are going to refer to the most common case a stem with exactly 2 lines. The solutions of linear equations will generate values which when substituted for the unknown values make the equation true. In the case of one variable there is only one solution such as x 2 0. Answer by emargo19 101 show source.