The coordinates are the best estimate of the solution to the system of equations is (-1, 0) . Therefore , (-1, 0) is correct .
Here's how we can find the solution:
Convert the equations to slope-intercept form:
The first equation, −3x+y=2, can be rewritten as y=3x+2.
This equation has a slope of 3 and a y-intercept of 2.
The second equation, −4x+7y=1, can be rewritten as y= 4/7x + 1/7 .
This equation has a slope of 4/7 and a y-intercept of 1/7.
Graph the equations:
Plot the y-intercepts for each equation. The y-intercept for the first equation is (0,2), and the y-intercept for the second equation is (0, 1/7 ).
Use the slopes to draw the lines. Remember that the slope tells you rise over run. For example, a slope of 3 means you rise 3 units for every 1 unit you run to the right.
Find the intersection point:
The lines intersect at the point where they cross each other. In this case, the lines intersect at (−1,0).
Therefore, the best estimate of the solution to the system of equations is (−1,0).
Here are the other answer choices and why they are not the best estimate:
(−1,−1): This point is below the line for the first equation, so it is not a solution.
(1,0): This point is to the right of the line for the second equation, so it is not a solution.
(1,−1): This point is below both lines, so it is not a solution.