That one, there!
You model your equation on a number line to using a bar model.
The coordinates of the point of intersection represents the solution to the linear equations.
If it is a linear system, then it could have either 1 solution, no solutions, or infinite solutions. To understand this, think of two lines (consider a plane which is just 2 dimensional - this represents 2 variables and 2 equations, but the idea can be extended to more dimensions).If the 2 lines intersect at a point, then that point represents a solution. If the lines are parallel, then they never intersect, and there is no solution. If the equations are such that they are just different ways of describing the same line, then they intersect at every point, so there are infinite solutions. If you have more than 2 lines then maybe some of them will intersect, but this is not a solution for the whole system. If all lines intersect at a single point, then that is the single solution for the whole system.If you have equations that describe something other than a straight line, then it's possible that they may intersect in more than one point.
No. Vertical lines and horizontal lines have undefined and 0 slopes. Undefined could be any number, so the answer is No. Good luck with your Apex :)
Any point on the line is a solution to the equation, and any solution to the equation is a point on the line. Ie any point where the y coordinate is 5 times the x coordinate will be on the line; for example the points (0, 0), (1, 5), (2, 10), (-1, -5), (-2, -10) all lines on the line y = 5x.
An equation will have one solution when it represents a line that intersects with another line at a single point, indicating a unique solution. It will have no solution if the lines are parallel, meaning they never intersect. An equation has infinitely many solutions when it represents the same line, where every point on the line is a solution. These scenarios typically apply to linear equations in two variables.
No, if two lines are parallel they will not have a solution.
the solution to a system is where the two lines intersect upon a graph.
extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.
To find the solution of two equations graphed on a coordinate plane, look for the point where the two lines intersect. This point represents the values of the variables that satisfy both equations simultaneously. The coordinates of this intersection point are the solution to the system of equations. If the lines are parallel, there is no solution; if they are the same line, there are infinitely many solutions.
No. A linear equation represents a straight line and the solution to a set of linear equations is where the lines intersect; two straight lines can only intersect at most at a single point - two straight lines may be parallel in which case they will not intersect and there will be no solution. With more than two linear equations, it may be that they do not all intersect at the same point, in which case there is no solution that satisfies all the equations together, but different solutions may exist for different subsets of the lines.
The solution to a system is an ordered pair (x,y) where the two lines intersect.
No, a linear equation in two variables typically has one unique solution, which represents the intersection point of two lines on a graph. However, if the equation represents the same line (as in infinitely many solutions) or if it is inconsistent (no solutions), then the type of solutions can vary. In general, a single linear equation corresponds to either one solution, no solutions, or infinitely many solutions when considering the same line.
A linear equation has one solution if its graph represents a straight line that intersects the coordinate plane at a single point. This occurs when the equation is in the form (y = mx + b), where (m) (the slope) is not equal to zero. Additionally, for a system of linear equations, if the equations represent lines with different slopes, they will intersect at exactly one point, indicating a unique solution.
Two lines with the same slope and y-intercept look like one single line. The "system" of equations consists of the same equation twice. The lines coincide at every point, which means there are an infinite number of solutions.
You get no solution if the lines representing the graphs of both equations have the same slope, i.e. they're parallel. "No solution" is NOT an answer.
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel