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What is a linear system?
A linear system is an equation to find the intersection of two or more lines. The equations are usually expressed with two variables, x and y. I don't know yet, but maybe geometry might have three variables, including z. Basically it's where two lines intersect and the most common ways of solving it are through graphing, substitution, and/or elimination.Presume you mean "linear".These are systems whose parameters vary directly or proportionally. Plotting functions results in straight lines.
What are two equations that intersect at -1 5 and how did you find this answer?
There is an infinite number of answers. Here is how to work it out The equation for any line is y = mx +c where m is the slope of the line and c, the point where the line crosses the y axis. Now put the point (-1, 5) into the equation: ==> 5 = -m +c ==> c = 5 +m Then just substitute different values for m (the slope) e.g. if the slope is 2, then c=7 so the line is y = 2x +7 e.g. if the slope is -6, then c = -1 so the line is y = -6x -1 These two lines intersect at (-1, 5) You can choose any slopes you like (including fractions) and you will get a pair of lines that intersect at (-1,5)
How do you know when an equation has infinitely many solutions How do you know when an equation has no solution?
You know that an equation has no solution when...Ex. 2>5 is falseTo show its false, put and O with a / through it----------To find it false, in terms of graphing, it is when you have parallel lines (Not crossing at any point if, in a perfect world, the lines went on forever).So for an exampley=2-3x6x+2y=7 (y=-3x+7/2 in Y=mx+b form)With this equation the lines do not pass through each other, and once more in a perfect world, if they kept going on the lines would never cross.
Yx-1 y-x 3 find the solution for the system?
y = x - 1 y - x = 3 y = x - 1 y = x + 3 Since both equations represent straight lines that have equal slopes, 1, then the lines are parallel to each other. That is that the lines do not intersect, and the system of the equations does not have a solution.
What are the solutions do these equations have x plus 3y equals 2 and 2x plus 6y equals -3?
None. If you rearrange each equation into slope intercept form ( y = mx + b), see below, you'll find that both equations have the same slope. Therefore they are parallel which also means would not intersect. Since the lines wouldn't intersect there is no solution to the system of equations.x + 3y = 23y = -x + 2y = (-1/3)x + 2/32x + 6y = -36y = -2x - 3y = (-1/3)x - (1/2)
