Question
Solve the system of equations by substitution. Use the sketch pad to show your work. 2 "x" minus 3 "y" equals negative 12x−3y=−1and "y" equals "x" minus 1y=x−1 2️⃣What is the value of x?
Answers
Answered by
GPT-4o mini
To solve the system of equations by substitution, we have the following equations:
1. \( 2x - 3y = -1 \)
2. \( y = x - 1 \)
**Step 1: Substitute \( y \) in Equation 1**
From Equation 2, we can substitute \( y \) in Equation 1:
\[
2x - 3(x - 1) = -1
\]
**Step 2: Simplify**
Now we simplify the equation:
\[
2x - 3x + 3 = -1
\]
Combine like terms:
\[
-1x + 3 = -1
\]
Subtract 3 from both sides:
\[
-1x = -1 - 3
\]
\[
-1x = -4
\]
Divide both sides by -1:
\[
x = 4
\]
**Step 3: Find the value of \( y \)**
Now that we have \( x = 4 \), we can find \( y \) using Equation 2:
\[
y = x - 1
\]
\[
y = 4 - 1
\]
\[
y = 3
\]
**Final Solution:**
Thus, the solution to the system of equations is \( x = 4 \) and \( y = 3 \).
If you want a visual representation, you could graph both equations on a coordinate plane to see where they intersect, but as a text-based model, that part is not possible here.
1. \( 2x - 3y = -1 \)
2. \( y = x - 1 \)
**Step 1: Substitute \( y \) in Equation 1**
From Equation 2, we can substitute \( y \) in Equation 1:
\[
2x - 3(x - 1) = -1
\]
**Step 2: Simplify**
Now we simplify the equation:
\[
2x - 3x + 3 = -1
\]
Combine like terms:
\[
-1x + 3 = -1
\]
Subtract 3 from both sides:
\[
-1x = -1 - 3
\]
\[
-1x = -4
\]
Divide both sides by -1:
\[
x = 4
\]
**Step 3: Find the value of \( y \)**
Now that we have \( x = 4 \), we can find \( y \) using Equation 2:
\[
y = x - 1
\]
\[
y = 4 - 1
\]
\[
y = 3
\]
**Final Solution:**
Thus, the solution to the system of equations is \( x = 4 \) and \( y = 3 \).
If you want a visual representation, you could graph both equations on a coordinate plane to see where they intersect, but as a text-based model, that part is not possible here.