$$ \begin{array}{l}y=5 x-3 \ x=y-5 \longrightarrow x=5 x-3-5 \ ext { (1)) What is one way you can use substitution to solve this problem? } \ ext { (1)) Substitute } 5 x-3 ext { for } y \ ext { (1) Now, find the solution to the system of equations, } \ (\square, \square)\end{array} $$ ?

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$$ \begin{array}{l}y=5 x-3 \ x=y-5 \longrightarrow x=5 x-3-5 \ 	ext { (1)) What is one way you can use substitution to solve this problem? } \ 	ext { (1)) Substitute } 5 x-3 	ext { for } y \ 	ext { (1) Now, find the solution to the system of equations, } \ (\square, \square)\end{array} $$ ?

UpStudy AI · Accepted Answer

To solve the system of equations using substitution, we will follow these steps:

1. **Identify the equations:**
   We have the following two equations:
   $$
   y = 5x - 3 \quad (1)
   $$
   $$
   x = y - 5 \quad (2)
   $$

2. **Substitute $$y$$ from equation (1) into equation (2):**
   We will substitute $$y$$ in equation (2) with the expression from equation (1):
   $$
   x = (5x - 3) - 5
   $$

3. **Simplify the equation:**
   Now, we simplify the equation:
   $$
   x = 5x - 3 - 5
   $$
   $$
   x = 5x - 8
   $$

4. **Rearrange the equation:**
   To isolate $$x$$, we can rearrange the equation:
   $$
   x - 5x = -8
   $$
   $$
   -4x = -8
   $$
   $$
   x = 2
   $$

5. **Substitute $$x$$ back to find $$y$$:**
   Now that we have $$x$$, we can substitute it back into equation (1) to find $$y$$:
   $$
   y = 5(2) - 3
   $$
   $$
   y = 10 - 3
   $$
   $$
   y = 7
   $$

6. **Final solution:**
   The solution to the system of equations is:
   $$
   (x, y) = (2, 7)
   $$

Thus, the final answer is $$(2, 7)$$.
The solution to the system of equations is $$ (2, 7) $$.

?

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