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This can happen in different ways:
a) More variables than equations. For instance, a single equation with two variables (such as x + y = 15), two equations with three variables, two equations with four variables, etc.
b) To of the equations describe the same line, plane, or hyper-plane - this, in turn, will result in that you "really" have less equations than it seems. For example:
y = 2x + 3
2y = 4x + 6
The second equation is simply the first equation multiplied by 2.
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What does it mean if there are an infinite number of solutions to a system of linear equations?
Any two numbers that make one of the equations true will make the other equation true.
What are the possible solutions for a system of equations?
The system of equations can have zero solutions, one solution, two solutions, any finite number of solutions, or an infinite number of solutions. If it is a system of LINEAR equations, then the only possibilities are zero solutions, one solution, and an infinite number of solutions. With linear equations, think of each equation describing a straight line. The solution to the system of equations will be where these lines intersect (a point). If they do not intersect at all (or maybe two of the lines intersect, and the third one doesn't) then there is no solution. If the equations describe the same line, then there will be infinite solutions (every point on the line satisfies both equations). If the system of equations came from a real world problem (like solving for currents or voltages in different parts of a circuit) then there should be a solution, if the equations were chosen properly.
A system of linear equation in two variables can have how many solutions?
None, one or an infinite number. In graph form, the three correspond to: None = Parallel lines One = Interscting lines Infinite = Coincident lines.
Which equation has a solution of -4?
There are an infinite number of equations with this solution, eg x = 6 - 10; x = 45678 - 45682; x squared = 16 etc etc
What is the discriminant and how is it used to solve equations using the quadratic formula?
It is not to solve so much as to see the number of solutions and whether there is a real solution to the equation. b2 - 4(a)(c) A positive answer = two real solutions. A negative answer = no real solution ( complex solution i ) If zero as the answer there is one real solution.
