Use the drop-down menus to complete the statements below to answer this question:

Question

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 (−6,4)
satisfy the equation y=13x+6
because (−6,4)

.

If (−6,4)
satisfies the equations of two lines, (−6,4)
is
, so the lines will
at (−6,4)
.

This means that if two lines
at (−6,4)
, then (−6,4)
is the
to the system of equations.

This means that if you substitute −6
for x
and 4
for y
in the equations, both equations will be

Answer 1

satisfied or true. Since the equations are satisfied by the same point, the lines will intersect at (-6,4). In other words, (-6,4) is the solution to the system of equations. Thus, by looking at the graph and identifying the point of intersection, we can determine whether a system of linear equations has a solution.