Table of Contents
- 1 How can you tell if a point is a solution to a system?
- 2 How can you determine the exact solution to this system of equations?
- 3 Which equation has exactly one solution?
- 4 How do you solve a system of linear equations in two variables?
- 5 What does it mean for an equation to have infinitely many solutions?
How can you tell if a point is a solution to a system?
A system of linear equations consists of the equations of two lines. The solution to a system of linear equations is the point which lies on both lines. In other words, the solution is the point where the two lines intersect.
How can you determine the exact solution to this system of equations?
To solve a system of equations by substitution, solve one of the equations for a variable, for example x. Then replace that variable in the other equation with the terms you deemed equal and solve for the other variable, y. The solution to the system of equations is always an ordered pair.
Which system of equations is inconsistent?
A system of two linear equations can have one solution, an infinite number of solutions, or no solution. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
Which equation has exactly one solution?
quadratic equation
Answer: If a quadratic equation has exactly one real number solution, then the value of its discriminant is always zero. A quadratic equation in variable x is of the form ax2 + bx + c = 0, where a ≠ 0.
How do you solve a system of linear equations in two variables?
Solving Systems of Equations in Two Variables by the Addition Method
- Write both equations with x– and y-variables on the left side of the equal sign and constants on the right.
- Write one equation above the other, lining up corresponding variables.
- Solve the resulting equation for the remaining variable.
What is example of inconsistent equations?
Inconsistent equations is defined as two or more equations that are impossible to solve based on using one set of values for the variables. An example of a set of inconsistent equations is x+2=4 and x+2=6.
What does it mean for an equation to have infinitely many solutions?
It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.