A system of equations will intersect at exactly one point if the equations represent two lines that are neither parallel nor coincident, meaning they have different slopes. In this case, there is a unique solution to the system. If the lines are parallel, they will not intersect at all, and if they are coincident, they will intersect at infinitely many points.
the solution to a system is where the two lines intersect upon a graph.
Parallel lines don't intersect, no matter how many of them there are.
In the same coordinate space, i.e. on the same set of axes: -- Graph the first equation. -- Graph the second equation. -- Graph the third equation. . . -- Rinse and repeat for each equation in the system. -- Visually examine the graphs to find the points (2-dimension graph) or lines (3-dimension graph) where all of the individual graphs intersect. Since those points or lines lie on the graph of each individual graph, they are the solution to the entire system of equations.
Yes, the graph of the equation ( y = ax ) will always intersect the origin (0,0) regardless of the value of ( a ). This is because when ( x = 0 ), the equation simplifies to ( y = a \cdot 0 = 0 ), indicating that the point (0,0) is always on the graph. Therefore, the graph will always pass through the origin.
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.
the solution to a system is where the two lines intersect upon a graph.
Parallel lines don't intersect, no matter how many of them there are.
-- Graph each equation individually. -- Examine the graph to find points where the individual graphs intersect. -- The points where the individual graphs intersect are the solutions of the system of equations.
In the same coordinate space, i.e. on the same set of axes: -- Graph the first equation. -- Graph the second equation. -- Graph the third equation. . . -- Rinse and repeat for each equation in the system. -- Visually examine the graphs to find the points (2-dimension graph) or lines (3-dimension graph) where all of the individual graphs intersect. Since those points or lines lie on the graph of each individual graph, they are the solution to the entire system of equations.
That's right. If a system of equations has a solution, then their graphs intersect, and the point where they intersect is the solution, because it's the point that satisfies each equation in the system. Straight-line graphs with the same slope are parallel lines, and they never intersect, which is another way of saying they have no solution.
Yes, the graph of the equation ( y = ax ) will always intersect the origin (0,0) regardless of the value of ( a ). This is because when ( x = 0 ), the equation simplifies to ( y = a \cdot 0 = 0 ), indicating that the point (0,0) is always on the graph. Therefore, the graph will always pass through the origin.
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.
Sometimes. Not always.
Write each equations in popular form. ... Make the coefficients of one variable opposites. ... Add the equations ensuing from Step two to remove one variable. Solve for the last variable. Substitute the answer from Step four into one of the unique equations.
You find the equation of a graph by finding an equation with a graph.
A table, graph, or equation represents a function if each input (or x-value) has exactly one output (or y-value). For a table, check that no x-value repeats with different y-values. In a graph, a vertical line drawn through any x-value should intersect the curve at most once. For an equation, it must pass the vertical line test when graphed, meaning it can be expressed in a form where every x-value corresponds to only one y-value.
When a system of linear equations is graphed, each equation is represented by a straight line on the coordinate plane. The solutions to each equation correspond to all the points on that line. The intersection points of the lines represent the solutions to the entire system; if the lines intersect at a point, that point is the unique solution. If the lines are parallel, there are no solutions, and if they overlap, there are infinitely many solutions.