Solving a system of three equations with infinite many solutions

👉Learn how to solve a system of three linear systems. A system of equations is a set of equations which are to be solved simultaneously. A linear equation is an equation whose graph is a straight line. The solution to a system of equations is a set of unique values of the variables for which each of the equation is satisfied.

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✅Solve a System of Equations With Three Variables

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[davidthaler]

You can almost tell how this will turn out just by looking.

If you divide all terms in the first equation by 2, the result is a copy of the third equation. Using the two identical equations to eliminate a variable cancels ALL terms to zero, leaving you with a single equation in 3 variables, which has an infinite number of solutions.

[rampantfox]

Your second analysis of why there are infinitely many solutions is not quite correct. You used equations 2 and 3 to eliminate y, but - x - z = 7 alone does not imply infinitely many solutions. If this system had a solution, and you were going to solve it using elimination, you could eliminate y using equations 2 and 3, but you would also have to eliminate y using a different pair of equations. If you were unlucky enough to use equations 1 and 2, you would get a second equation in x and z alone. You would then take your first equation (which you call equation B) and this second equation and solve a 2x2 system. THAT process would yield a 0 = 0 case, and hence infinitely many solutions.

[vandrickinman-benavente]

Well, you just saved my GPA by a full 2 points lol

[alexz]

Thats not really solving the system though thats just saying that it has infinite solutions and its dependent

[zxcvbnmaw]

You don't actually show how to solve this...

[carlosjoaquinsantos]

I got the vlue of x y and z
By multiplying the 1st equation by 3 and the 2nd Equation I multiplied it by -2

[sanju.]

You could solve it easily with Cramer's Rule