Question

The graph shows one of the linear equations for a system of equations. Which equation represents the second linear equation for the system of equations that has the solution which corresponds to a point at (120, -43)?

A) 3 4 x - 2y = 4
B) 2 3 x + 2y = 6
C) 3 4 x + 2y = -4
D) 2 3 x + 2y = -6

Answer 1

The correct linear equation that forms a system with a given line which intersects at the point (120, -43) is Option C: ¾ x + 2y = -4. This answer used substitution to test the given coordinates in each option's equation to find the correct one.

Step-by-step explanation:

The student is asking which linear equation from a given list of options forms a system with an existing line that intersects at the point (120, -43). To determine which equation corresponds to this point, we need to substitute the coordinates into each equation and see which equation is true with those values.

For example, let's substitute the x-value of 120 and the y-value of -43 into the first option (A).

• Option A: ¾ × 120 - 2(-43) = 90 + 86 = 176, which is not equal to 4. So, option A is not the solution.

• Option B: ¾ × 120 + 2(-43) = 90 - 86 = 4, which is not equal to 6. Therefore, option B is also not the solution.

• Option C: ¾ × 120 + 2(-43) = 90 - 86 = 4, which is equal to -4. Therefore, option C is the correct solution.

• Option D: ¾ × 120 + 2(-43) = 80 - 86 = -6, which is also not correct.

Therefore, the equation that represents the second linear equation of the system with the solution corresponding to the point (120, -43) is Option C: ¾ x + 2y = -4.