Section 4.5 - Solving A Linear System Graphically

Parallel lines will have no points of intersection because they are always equidistant and never meet, no matter how far they are extended. This is a fundamental property of parallel lines in Euclidean geometry.

The given relation is x + 2y = 6. To find the relation that intersects this at (2, 2), we substitute x = 2 and y = 2 into each of the answer choices.

For 6x + y = 2, substituting x = 2 and y = 2 gives 12 + 2 = 2 which is not true.

For 2x + y = 4, substituting x = 2 and y = 2 gives 4 + 2 = 4 which is not true.

For x + y = 4, substituting x = 2 and y = 2 gives 2 + 2 = 4 which is true.

For x + y = 2, substituting x = 2 and y = 2 gives 2 + 2 = 2 which is not true.

Therefore, the relation x + y = 4 is the correct answer as it intersects the given relation at (2, 2).

To break even, Andrew needs to earn back the total cost he incurred. The cost per can is $0.25 and he needs to sell each can for $0.50. Therefore, he makes a profit of $0.25 per can sold. By dividing the total cost of $5.00 by the profit per can ($0.25), we can determine the number of cans needed to break even. $5.00 / $0.25 = 20 cans. Hence, Andrew needs to sell 20 cans to break even.

The given lines 3x - 2y = 5 and 6x - 4y = 6 are parallel to each other, meaning they will never intersect. Therefore, the correct answer is "none".

To determine the point of intersection of the lines x + y = 8 and y = x + 4, we can substitute the value of y from the second equation into the first equation. By doing so, we get x + (x + 4) = 8, which simplifies to 2x + 4 = 8. Solving for x, we find x = 2. Substituting this value back into the second equation, we get y = 2 + 4 = 6. Therefore, the point of intersection is (2, 6).

The charge for A-1 plumbing is $75 plus $50 per hour, while Plumbing Masters charges $100 plus $25 per hour. To find the point at which the charges are the same for both companies, we need to set up an equation. Let x be the number of hours. The equation would be 75 + 50x = 100 + 25x. Simplifying this equation, we get 25x = 25, which means x = 1. Therefore, the charge is the same for both companies after 1 hour.

If the person is going to use less than 100 minutes, it would be more cost-effective to choose Cheap Cell Phones since they do not have a flat fee and charge $0.25 per minute. However, if the person is going to use more than 100 minutes, Basic Cell Phones would be a better option as they have a flat fee of $15 and charge $0.10 per minute.

To determine the point of intersection of the two lines, we can solve the system of equations formed by the two lines. By substituting the value of y from the first equation into the second equation, we get 2x + 3x + 5 = 10. Simplifying this equation gives us 5x + 5 = 10. Solving for x, we find that x = 1. Substituting this value of x back into the first equation, we can solve for y and find that y = 8. Therefore, the point of intersection is (1, 8).

The given lines are y = 4 and x = 3. The line y = 4 is a horizontal line passing through the y-coordinate 4. The line x = 3 is a vertical line passing through the x-coordinate 3. These two lines intersect at the point (3, 4), as the x-coordinate of the intersection point is 3 and the y-coordinate is 4. Therefore, the correct answer is (3, 4).

The equation y = 10x represents the price at which the school store sells each shirt, with y being the price and x being the number of shirts. The equation y = 3x + 25 represents the cost to the store to purchase each shirt from the supplier, with y being the cost and x being the number of shirts. By setting up these two equations, we can represent the situation where the store charges $10 per shirt and pays $3 per shirt plus a one-time set up fee of $25 to the supplier.