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Wolfram|Alpha is capable of solving a wide variety of systems of equations. It can solve systems of linear equations or systems involving nonlinear equations, and it can search specifically for integer solutions or solutions over another domain.
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
A system of linear equations has one solution when the graphs intersect at a point. No solution. A system of linear equations has no solution when the graphs are parallel.
Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines, there can be no solution. This is called an "inconsistent" system of equations, and it has no solution. The third graph above, "Case 3", appears to show only one line.
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
The most simple method for solving systems of equations is to transform one of the equations so it allows for the canceling out of a variable. In this case, we can multiply \\displaystyle 3x + y = 8 by to get . Then, we can add \\displaystyle 2x + 4y = 12 to this equation to yield , so .
There are three possible outcomes for a system of linear equations: one unique solution, infinitely many solutions, and no solution.
Step 2: Solve for x. Step 3: To find the y-value, substitute in 3 for x in one of the equations. Step 4: Solve for y. Step 5: Identify the solution as an ordered pair. What if adding or subtracting does not eliminate a variable? Example. 3x y = 8. x + 2y = 5.
The solution is the point of intersection between the lines in the equation. Parallel lines have no solution, that is, they never intersect. Dependent systems are the same line so every solution of the first line is a solution of the other line, hence infinite number of solutions.
Solve for x2 or y2 in one of the given equations. ... Substitute the value from Step 1 into the other equation. ... Solve the quadratic equation. ... Substitute the value(s) from Step 3 into either equation to solve for the other variable.
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