Answer:
Line y = −1/2x + 9 intersects line y = x + 7.
Explanation:
To find the solution to the system of equations, we can set the two equations equal to each other:
-1/2x + 9 = x + 7
Solving for x, we get:
-3/2x = -2
x = 4/3
Substituting this value of x into either equation, we can solve for y:
y = (-1/2)(4/3) + 9 = 17/3
Therefore, the solution to the system of equations is the ordered pair (4/3, 17/3).
Now, to determine which description best describes the solution, we can analyze each option:
Lines y = −1/2x + 9 and y = x + 7 intersect the x-axis.
Option 1 is not true, as neither of the lines intersect the x-axis.
Lines y = −1/2x + 9 and y = x + 7 intersect the y-axis.
Option 2 is not true, as neither of the lines intersect the y-axis.
Line y = −1/2x + 9 intersects the origin.
Option 3 is not true, as the line y = −1/2x + 9 does not pass through the origin.
Line y = −1/2x + 9 intersects line y = x + 7.
Option 4 is true, as we found that the two lines intersect at the point (4/3, 17/3).
Therefore, the correct answer is: Line y = −1/2x + 9 intersects line y = x + 7.
I hope this helps you! :))