The coordinates below represent two linear equations.
How many solutions does this system of equations have?
Line 1
x y
–2 7
0 6
Line 2
x y
3 0
0 –3
A. 0
B. exactly 1
C. exactly 2
D. infinitely many
You could graph these points and extend a line through the points to see if the lines cross at one point that would give you one answer.
Since the problem states that they are linear, they won't have 2 answers.
If the lines are parallel, no solution.
If they really are the same line, one line will be on top of the other and they have infinite solutions.
Another way is to write the equation of each line by using the two points given. You should find the slope first and then y=mx+b to find the equation.
To determine the number of solutions for this system of equations, we need to analyze the relationship between the two lines represented by the given coordinates.
One approach is to plot the points given for each line on a coordinate plane and observe their relationship.
For Line 1:
The points (-2, 7) and (0, 6) form a line. Plotting these points and connecting them, we can see that Line 1 is a straight line that slopes slightly downward from left to right.
For Line 2:
The points (3, 0) and (0, -3) form a line. Plotting these points and connecting them, we can see that Line 2 is a straight line that slopes upward from left to right.
Now, it is important to consider the intersection of the two lines:
From the plotted lines, we can observe that Line 1 and Line 2 intersect at a single point (0, 6). This means that the two lines intersect at only one location.
Therefore, the system of linear equations represented by the coordinates has exactly 1 solution.
The correct answer is B. exactly 1.