Question

Consider the following system of equations.

Line 1: ʹ2x-y=-3
Line 2: -6x-2y=-6
Part A: Is [0.3] a solution to Line 1? Explain your answer.
Part B: Coordinate [0.-3] is a solution to Line 2.
Part C: What are the slopes of Line1 and Line 2? Part
Part D: What are the y -intercepts of Line 1 and Line 2
E: Sketch the graph of Line 1 and Line 2.
F: What is the solution to the graph."

Answer 1

In Part A, [0.3] is not a solution to Line 1. In Part B, (-3, 0) is not a solution to Line 2. In Part C, the slopes of Line 1 and Line 2 are 2 and 3, respectively.

Step-by-step explanation:

Part A: To determine if [0.3] is a solution to Line 1, substitute the values of x and y into the equation: 2(0.3) - y = -3. Simplifying, we get 0.6 - y = -3. Solving for y, we subtract 0.6 from both sides and find that y = 3.6. Therefore, [0.3] is not a solution to Line 1.

Part B: To determine if (-3, 0) is a solution to Line 2, substitute the values of x and y into the equation: -6(-3) - 2(0) = -6. Simplifying, we get 18 = -6, which is not true. Therefore, (-3, 0) is not a solution to Line 2.

Part C: The slope of Line 1 can be found by rearranging the equation into slope-intercept form, y = mx + b, where m is the slope. Line 1 becomes y = 2x + 3. Thus, the slope of Line 1 is 2. Similarly, Line 2 can be rearranged into slope-intercept form, y = mx + b, where m is the slope. Line 2 becomes y = 3x + 3. Therefore, the slope of Line 2 is 3.

Part D: The y-intercept of Line 1 can be found by setting x to 0 in the equation of Line 1: 2(0) - y = -3. Simplifying, we find that -y = -3, and solving for y, we get y = 3. Therefore, the y-intercept of Line 1 is 3. Similarly, the y-intercept of Line 2 can be found by setting x to 0 in the equation of Line 2: -6(0) - 2y = -6. Simplifying, we find that -2y = -6, and solving for y, we get y = 3. Therefore, the y-intercept of Line 2 is also 3.

Part E: Please note that as a text-based platform, we are unable to sketch graphs. However, you can manually sketch Line 1 and Line 2 on a graph using the slope and y-intercept values we have determined above.

Part F: The solution to the system of equations represented by Line 1 and Line 2 can be found by solving the equations simultaneously. By substituting Line 1's equation into Line 2, we get: -6x - 2(2x + 3) = -6. Simplifying, we find that -10x - 6 = -6. Solving for x, we get x = 0. Substituting this value of x back into Line 1's equation, we find that y = 3. Therefore, the solution to the system of equations is (0, 3).