Answered

Using the graphing function on your calculator, find the solution to the system of equations shown below.

[tex]\[
\begin{array}{l}
y - 3x = 1 \\
y - 5x = -3
\end{array}
\][/tex]

A. No solution
B. [tex]\(x = 2, y = 7\)[/tex]
C. [tex]\(x = 7, y = 2\)[/tex]
D. More than 1 solution



Answer :

GinnyAnswer
To solve the system of equations:
[tex]\[ \begin{cases} y - 3x = 1 \\ y - 5x = -3 \end{cases} \][/tex]

we'll proceed through a sequence of steps to find the solution.

### Step-by-Step Solution:

1. Rewrite the equations for clarity:
[tex]\[ \begin{cases} y = 3x + 1 \quad \text{(Equation 1)} \\ y = 5x - 3 \quad \text{(Equation 2)} \end{cases} \][/tex]

2. Set the equations equal to each other since both are equal to [tex]\( y \)[/tex]:
[tex]\[ 3x + 1 = 5x - 3 \][/tex]

3. Solve the equation for [tex]\( x \)[/tex]:
- Subtract [tex]\( 3x \)[/tex] from both sides:
[tex]\[ 1 = 2x - 3 \][/tex]
- Add 3 to both sides:
[tex]\[ 4 = 2x \][/tex]
- Divide by 2:
[tex]\[ x = 2 \][/tex]

4. Substitute the value of [tex]\( x \)[/tex] back into one of the original equations to find [tex]\( y \)[/tex]. We'll use Equation 1 for this purpose:
[tex]\[ y = 3(2) + 1 \][/tex]
[tex]\[ y = 6 + 1 \][/tex]
[tex]\[ y = 7 \][/tex]

So, the solution to the system of equations is:
[tex]\[ x = 2 \quad \text{and} \quad y = 7 \][/tex]

### Final Answer:

The correct answer is:
B. [tex]\( x = 2, y = 7 \)[/tex]

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