Exercises: graphically solving systems of equations
Decide whether the following systems of linear equations are solvable or not. Make a sketch of the corresponding linear functions.
For this task you need the following basic knowledge: System of linear equations
solve for
solve for
Draw both straight lines in a coordinate system
Answer
The linear system of equations has exactly one solution, since the two straight lines intersect at the point .
First, solve the equations and for and draw the corresponding straight lines into a coordinate system.
For this task you need the following basic knowledge: System of linear equations
solve for
solve for
Draw both straight lines in a coordinate system (both lines are the same)
Answer
The linear system of equations has infinitely many solutions.
The equations (\text{I}) and (\text{II}) describe the same linear function. Therefore, for each x\text{I} (x|y)=(x|-4x+8) is a solution of the linear system of equations.
First solve the equations and for and draw the corresponding straight lines into a coordinate system.
For this task you need the following basic knowledge: System of linear equations
solve for
solve for
Draw both straight lines in a coordinate system (both lines are parallel, as they have the same slope)
Answer
The linear system of equations has no solution
The corresponding straight lines resulting from the linear system of equations are parallel to each other and do not intersect.
First solve the equations and for and draw the corresponding straight lines into a coordinate system.
For this task you need the following basic knowledge: System of linear equations
solve for
solve for
Draw both straight lines in a coordinate system
Answer
The linear system of equations has exactly one solution, since the two straight lines intersect at the point .
First solve the equations and for y and draw the corresponding straight lines into a coordinate system.
For this task you need the following basic knowledge: System of linear equations
solve for
solve for
Draw both straight lines in a coordinate system
Answer
The linear system of equations has exactly one solution, since the two straight lines intersect at the point .
First solve equations and for y and draw the corresponding straight lines into a coordinate system.
For this task you need the following basic knowledge: System of linear equations
solve for
solve for
Draw both straight lines in a coordinate system
Answer
The linear system of equations has exactly one solution, since the two straight lines intersect at the point .
First solve equations and for y and draw the corresponding straight lines into a coordinate system.