What are the advantages and disadvantages of solving linear equations in two variables by graphing?
The advantage of solving a system of linear equations by graphing is that it is relatively easy to do and requires very little algebra, and the main disadvantage is that your answer will be approximate due to having to read the answer from a graph.
How does graphing help you solve a system of linear equations?
To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect. The two lines intersect in (-3, -4) which is the solution to this system of equations.
When solving a system of linear equations by graphing how do you know if the system has no solution?
| One Solution | No Solutions |
|---|---|
| If the graphs of the equations intersect, then there is one solution that is true for both equations. | If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations. |
Which equations has only one solution?
An independent system of equations has exactly one solution (x,y) . An inconsistent system has no solution, and a dependent system has an infinite number of solutions.
How do you know if a system of equations has one solution?
When both equations have the same slope, but not the same y-intercept, they’ll be parallel to each other and no intersections means no solutions. When both equations have different slopes than regardless of the y-intercept they’ll intersect for certain, therefore it has exactly one solution.
What lines have infinite solutions?
A system of linear equations has no solution when the graphs are parallel. Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.
How do you solve linear equations with infinite solutions?
In this case, the idea is that you have to create something that makes both the right side of the equation and the left side to be equal to each other which gives you an infinite number of solutions. so if you have 5x-8 on the left, you need 5x-8 on the right for everything to cancel and end up with 0=0.
How do you tell if a system of linear equations has infinitely many solutions?
If a system has infinitely many solutions, then the lines overlap at every point. In other words, they’re the same exact line! This means that any point on the line is a solution to the system.
When a linear equation has no solution?
A system of linear equations can have no solution, a unique solution or infinitely many solutions. A system has no solution if the equations are inconsistent, they are contradictory. for example 2x+3y=10, 2x+3y=12 has no solution. is the rref form of the matrix for this system.
What is the condition for parallel lines in linear equations?
If two lines are parallel then, they have no solution pair of linear equations is inconsistent; If two lines are coincident then, they have infinite solution and pair of linear equations is consistent; If two lines are intersecting then, they have unique solution and pair of linear equations is consistent.
What is unique solution in linear equation?
Condition for Unique Solution to Linear Equations A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point. i.e., if the two lines are neither parallel nor coincident.
How many solutions does the pair of equations?
Answer: The pair of equation of lines do not have any solution. Since the both equation of lines have same slope it shows that both the lines are parallel to each other and we know that the parallel lines never intersect with other so both the pair of equation of lines do not have any solution.
How many solutions does pair of equations y 0 and y =- 5 has?
question_answer Answers(2) Hence they do not have solution. Solution: Y= 0 is the equation of x axis and y = -5 is the line which is parallel to x axis. It has no solutions since the given equations are parallel .
How many solutions does the pair of equations y 0 and y has?
Accepted Answer: A pair of equations y = 0 and y = -5 has no solution They are parallel.
How many solutions does the pair of equations y 0 and y =- 3 have?
Answer. They have no solution because two values of y can’t be possible.
How many solutions does the pair of equations y 0 and y =- 7 has?
Graphically y = 0 is a straight line which is x – axis and y = – 7 is a straight line parallel to x – axis, 7 units below the origin therefore lines y = 0 and y = – 7 are parallel. ∴ They have no solution.
What will be the degree of linear equations in two variables?
Answer: The degree of a linear equation in two variables is ( D) 2.
How many solutions does a pair of equation y equal to 0 and y equal minus 5 have?
Answer. Answer: The pair of linear equation y=0 and y = -5 has no solution and lines are parallel and distance between them is 5 unit.
For what value of p does the pair of equations?
Hence the given pair of equation has unique solution for all values of p except 4.
What is the highest degree of linear equations in two variables?
An algebraic equation, such as y = 2x + 7 or 3x + 2y – z = 4, in which the highest degree term in the variable or variables is of the first degree. The graph of such an equation is a straight line if there are two variables.