Which system of equations has the same solution as the system below? 3x+3y=8 2x-y=5 solve this for me

We are given the system of equations:

\[
3x + 3y = 8 \quad \text{(1)}
\]
\[
2x - y = 5 \quad \text{(2)}
\]

### Step 1: Solve one of the equations for one variable.

Let's start by solving Equation (2) for \(y\). From Equation (2):
\[
2x - y = 5
\]
Solving for \(y\):
\[
y = 2x - 5
\]

### Step 2: Substitute \(y = 2x - 5\) into Equation (1).

Substitute \(y = 2x - 5\) into Equation (1):
\[
3x + 3(2x - 5) = 8
\]
Simplify:
\[
3x + 6x - 15 = 8
\]
\[
9x - 15 = 8
\]
Now, solve for \(x\):
\[
9x = 8 + 15
\]
\[
9x = 23
\]
\[
x = \frac{23}{9}
\]

### Step 3: Substitute \(x = \frac{23}{9}\) back into the expression for \(y\).

Now substitute \(x = \frac{23}{9}\) into \(y = 2x - 5\):
\[
y = 2\left(\frac{23}{9}\right) - 5
\]
\[
y = \frac{46}{9} - \frac{45}{9}
\]
\[
y = \frac{1}{9}
\]

### Final Solution:
The solution to the system of equations is:
\[
x = \frac{23}{9}, \quad y = \frac{1}{9}
\]

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Would you like more details on any step? Let me know if you need further explanation!

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1. How can you solve a system of equations using substitution?
2. How do you solve a system of equations using elimination?
3. What is the graphical interpretation of solving a system of linear equations?
4. How would you solve this system if the coefficients of \(x\) and \(y\) were fractions?
5. How can you check the solution of a system of linear equations?

**Tip:** Always double-check your solution by plugging values of \(x\) and \(y\) back into both original equations to verify the solution.

Which system of equations has the same solution as the system below? 3x+3y=8, 2x-y=5

Learn how to solve the system of equations 3x + 3y = 8 and 2x - y = 5 using the substitution method. This step-by-step guide explains how to find the solution for x and y, including detailed calculations and explanations. Ideal for students in Grades 8-10.

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