Question

Consider the following system of equations made up of Line 1 and Line 2.

Line 1: -2x - 2y = 4
Line 2: x + 5y = 10
Which of the following statements are true?
a) The solution is (2, 0).
b) The lines are parallel, and there is no solution.
c) The lines intersect at (2, 0).
d) The lines intersect at (0, 2).

Answer 1

The solution to the system of equations is (-5, 3), which means all the statements listed in the question are incorrect. The lines intersect at the point (-5, 3), not at (2, 0) or (0, 2), nor are the lines parallel.

Step-by-step explanation:

To solve the system of equations given by Line 1: -2x - 2y = 4 and Line 2: x + 5y = 10, we can use either the substitution or elimination method. Let's use the elimination method:

1. First, simplify Line 1, dividing the entire equation by -2, getting x + y = -2.
2. Now we have a new system of equations:
   
3. Subtract Line 1 from Line 2 to eliminate x: which results in 4y = 12, then solve for y to get y = 3.
4. Substitute y = 3 into Line 1, resulting in x + 3 = -2 and solve for x to get x = -5.

The solution to the system is (-5, 3). Therefore, statements a), b), c), and d) from the original question are all incorrect. The lines are neither parallel nor do they intersect at the given points. The correct solution intersects at the point (-5, 3).