Question

Solve the system of equations.

y=|x|−1


y=x+3


Use the image to answer the question.

The coordinate grid has x and y axes labeled from negative 5 to 5.

(1 point)
The solution is
,
.

Answer 1

To solve the system of equations given by:

1. \( y = |x| - 1 \)
2. \( y = x + 3 \)

we need to find the points where these two graphs intersect.

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

\[
|x| - 1 = x + 3
\]

### Step 2: Solve the absolute value equation:

#### Case 1: \( x \geq 0 \)
In this case, \( |x| = x \). The equation becomes:

\[
x - 1 = x + 3
\]

Subtracting \( x \) from both sides:

\[
-1 = 3
\]

This is not true, so there are no solutions in this case.

#### Case 2: \( x < 0 \)
In this case, \( |x| = -x \). The equation becomes:

\[
-x - 1 = x + 3
\]

Adding \( x \) to both sides:

\[
-1 = 2x + 3
\]

Subtracting 3 from both sides:

\[
-4 = 2x
\]

Dividing by 2:

\[
x = -2
\]

### Step 3: Find \( y \) using either original equation:

Using \( y = x + 3 \):

\[
y = -2 + 3 = 1
\]

### Conclusion:

The solution to the system of equations is:

\[
\boxed{(-2, 1)}
\]

Thus, the intersection point, or the solution to the system, is at \((-2, 1)\).