Question

1. use your knowledge of systems of equations and linear functions to answer the question below. show your work
2. \\(\

$$\begin{cases}3x + y = 25\\\\y = x - 3\\end{cases}$$

\\)
substitute \\(\underline{\quad\quad\quad\quad\quad\quad}\\) for \\(y\\) in the first equation.
\\(3x + (\underline{\quad\quad\quad}) = 25\\)
\\(\underline{\quad\quad\quad} - 3 = 25\\)
\\(\underline{\quad\quad\quad} + 3\quad\quad +3\underline{\quad\quad}\\)
\\(\underline{\quad\quad\quad}\quad\quad = 28\\)
\\(\underline{\quad\quad\quad}\quad\quad = \underline{\quad\quad\quad}\\)
since \\(x = \underline{\quad\quad\quad}\\), substitute \\(\underline{\quad\quad\quad}\\) for \\(x\\) in one of the equations to find the value of \\(y\\)
\\(y = x - 3\\)
\\(y = \underline{\quad\quad\quad} - 3\\)
\\(y = \underline{\quad\quad\quad}\\)
solution: \\( (\underline{\quad\quad\quad}, \underline{\quad\quad\quad}) \\)

Explanation:

Step1: Substitute \( y = x - 3 \) into the first equation

We know from the second equation that \( y = x - 3 \). So we substitute this expression for \( y \) in the first equation \( 3x + y = 25 \).
\( 3x + (x - 3) = 25 \)

Step2: Simplify the left - hand side

Combine like terms: \( 3x+x-3=4x - 3 \), so the equation becomes \( 4x-3 = 25 \)

Step3: Solve for \( x \)

Add 3 to both sides of the equation: \( 4x-3 + 3=25 + 3 \)
Simplify: \( 4x=28 \)
Divide both sides by 4: \( x=\frac{28}{4}=7 \)

Step4: Substitute \( x = 7 \) into the second equation to find \( y \)

We use the equation \( y=x - 3 \). Substitute \( x = 7 \) into it: \( y=7-3 \)
Simplify: \( y = 4 \)

Answer:

The solution of the system of equations \(

$$\begin{cases}3x + y=25\\y=x - 3\end{cases}$$

\) is \(x = 7,y = 4\) or the ordered pair \((7,4)\)

For the blanks:

• Substitute \(\boldsymbol{x - 3}\) for \(y\) in the first equation.
• \(3x+( \boldsymbol{x - 3})=25\)
• After combining like terms: \(4x-3 = 25\)
• Then \(4x-3+3=25 + 3\) (i.e., \(4x=28\))
• \(x=\boldsymbol{7}\)
• Substitute \(\boldsymbol{7}\) for \(x\) in \(y=x - 3\)
• \(y=\boldsymbol{7}-3\)
• \(y=\boldsymbol{4}\)
• Solution: \(\boldsymbol{(7,4)}\)