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What is a solution to a system of equations graphically?
Graphically, it is the point of intersection where the lines (in a linear system) intersect. If you have 2 equations and two unknowns, then you have a 2 lines in a plane. The (x,y) coordinates of the point where the 2 lines intersect represent the values which satisfies both equations. If there are 3 equations and 3 unknowns, then you have lines in 3 dimensional space. If all 3 lines intersect at a point then there is a solution to the system. With more than 3 variables, it is difficult to visualize more dimensions, though.
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.
How many solutions is it possible for a system of linear equations to have?
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
Can a linear system have exactly two solutions?
NO! A linear system can only have one solution (the lines intersect at one point), no solution (the lines are parallel), and infinitely many solutions (the lines are equivalent).
How many solutions are there when two lines have different slopes and y-intercepts?
If they are straight lines, then one solution.
