Use the drop-down menus to complete the statements below to answer this question:
Can you determine whether a system of linear equations has a solution just by looking at the graph of the equations?
CLEAR CHECK
The coordinates of a point satisfy the equation of a line if the point is
.
If a single point satisfies the equations of two lines, the point is
, so the lines will
at that point.
This means that each point where the two lines
is a
to the system of equations.
This means that if you substitute the x
- and y
-values of the point for x
and y
in the equations, both equations will be
.
Can you determine whether a system of linear equations has a solution just by looking at the graph of the equations?
CLEAR CHECK
The coordinates of a point satisfy the equation of a line if the point is ON the line.
If a single point satisfies the equations of two lines, the point is ON the lines, so the lines will INTERSECT at that point.
This means that each point where the two lines INTERSECT is a SOLUTION to the system of equations.
This means that if you substitute the x- and y-values of the point for x and y in the equations, both equations will be SATISFIED.