Question
19) Solve the system by substitution. \( \left\{\begin{array}{l}y=3 x+1 \\ y=5 x-3\end{array}\right. \)
Ask by Romero Cruz. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution is \( x = 2 \) and \( y = 7 \).
Solution
To solve the system of equations by substitution:
\[
\begin{cases}
y = 3x + 1 \\
y = 5x - 3
\end{cases}
\]
**Step 1:** Since both equations are equal to \( y \), set them equal to each other:
\[
3x + 1 = 5x - 3
\]
**Step 2:** Solve for \( x \):
\[
3x + 1 = 5x - 3 \\
1 + 3 = 5x - 3x \\
4 = 2x \\
x = 2
\]
**Step 3:** Substitute \( x = 2 \) back into one of the original equations to find \( y \). Using the first equation:
\[
y = 3(2) + 1 \\
y = 6 + 1 \\
y = 7
\]
**Solution:** The system has a unique solution at \( (x, y) = (2, 7) \).
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
To solve the system by substitution, we start with the first equation: \( y = 3x + 1 \). We can substitute this expression for \( y \) into the second equation: \( 3x + 1 = 5x - 3 \). Next, rearrange the equation to isolate \( x \): 1. Subtract \( 3x \) from both sides: \( 1 = 5x - 3x - 3 \) 2. This simplifies to: \( 1 = 2x - 3 \) 3. Add 3 to both sides: \( 4 = 2x \) 4. Finally, divide by 2: \( x = 2 \). Now, substitute \( x = 2 \) back into the first equation to find \( y \): \( y = 3(2) + 1 = 6 + 1 = 7 \). Thus, the solution to the system is \( (x, y) = (2, 7) \).
