Linear Algebra

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It is not possible to tell. The lines could intersect, in pairs, at several different points giving no solution. A much less likely outcome is that they all intersect at a single point: the unique solution to the system.

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0The slopes (gradients) of the two equations are different.

TWO linear equations with different slopes intersect in one point, regardlessof their y-intercepts. That point is the solution of the pair.However, this does not mean that three (or more) equations in two variables, even if they meet the above conditions, have a solution.

The question makes little general sense because the concept of slopes is appropriate when dealing with equations in only two variables.Assuming, therefore, that there are only two variables, then either the slopes are the same or they are different,If the slopes are the same and the intercepts are the same: there are infinitely many solutionsIf the slopes are the same and the intercepts are different: there are no solutionsIf the slopes are different: there is a unique solution.

Actually not. Two linear equations have either one solution, no solution, or many solutions, all depends on the slope of the equations and their intercepts. If the two lines have different slopes, then there will be only one solution. If they have the same slope and the same intercept, then these two lines are dependent and there will be many solutions (infinite solutions). When the lines have the same slope but they have different intercept, then there will be no point of intersection and hence, they do not have a solution.

Two linear equations (or lines) with the same y-intercept and different slopes are intersecting lines. They intersect at the y-intercept. If the slopes are negative reciprocals (ex: one slope is 3 and one slope it -1/3) then they are perpendicular lines.

The graph of a system of equations with the same slope will have no solution, unless they have the same y intercept, which would give them infinitely many solutions. Different slopes means that there is one solution.

It is a correct statement.

If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.

If the slopes of a straight line equation are the same but with different y intercepts then they are parallel.

When (the graph of the equations) the two lines intersect. The equations will tell you what the slopes of the lines are, just look at them. If they are different, then the equations have a unique solution..

The general form of an equation for a line isaX + bY = c.Since perpendicular lines have different slopes and different x and y intercepts the parameters a, b, and c are different for perpendicular lines

If they are straight lines, then one solution.

No the only time that a system of equations would have no solutions is when the two equations have the same slope but different y-intercepts which would mean that they are parallel lines. However, if they have different slopes and different y-intercepts than the solution would be where the two lines intersect.

There are several ways to find this out; for example, assuming the equations are in "x" and "y", and you put the equation in slope-intercept form (solve them for "y"), they will have different slopes. There is also a method based on determinants - some determinant must be non-zero.

Two parallel lines have equal slopes.

a and b are constants (and c is too). You can substitute any set of three real numbers for these letters, and you will still have an equation for a line. However, different values will result in different slopes and positions for the line. In fact, the values of a, b, and c are what determine the shape of the line.

Slopes have the same friction of the road but in slopes the Potential energy changes into Kinetic Energy which causes movement..

No they don't, the only thing that's different if that there using a different pieces of equipment that they like or are comfortable with to go down the slopes.

When their slopes are of the same value and their y intercepts are different

They are not parallel.

A straight line cannot have two slopes. A curve, however, might have a different slope at every different point.

7/12 and 7/12 is the answer

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