To solve the system of equations y = |x| and y = 2x + 3, we need to find the values of x and y that satisfy both equations simultaneously.

Step 1: Set the two equations equal to each other:

|x| = 2x + 3

Step 2: Solve for x. Since |x| is always positive or zero, and 2x + 3 is positive when x -1.5, we'll break this into two cases:

Case 1: x = 2x + 3, which simplifies to -x = 3, so x = -3. However, this doesn't satisfy x -1.5, so it's not a valid solution.

Case 2: -x = 2x + 3, which simplifies to 3x = -3, so x = -1.

Step 3: Substitute x = -1 into the original equations to solve for y:

y = |-1| = 1
y = 2(-1) + 3 = 1

So, the solution to the system of equations is (-1, 1), which corresponds to answer choice (a).

Question

To solve the system of equations y = |x| and y = 2x + 3, we need to find the values of x and y that satisfy both equations simultaneously.

Step 1: Set the two equations equal to each other:

|x| = 2x + 3

Step 2: Solve for x. Since |x| is always positive or zero, and 2x + 3 is positive when x > -1.5, we'll break this into two cases:

Case 1: x = 2x + 3, which simplifies to -x = 3, so x = -3. However, this doesn't satisfy x > -1.5, so it's not a valid solution.

Case 2: -x = 2x + 3, which simplifies to 3x = -3, so x = -1.

Step 3: Substitute x = -1 into the original equations to solve for y:

y = |-1| = 1
y = 2(-1) + 3 = 1

So, the solution to the system of equations is (-1, 1), which corresponds to answer choice (a).

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