Sure! Let's solve the system of linear equations step-by-step:
Given the system of equations:
1. \( 2y = x + 10 \)
2. \( 3y = 3x + 15 \)
### Step 1: Simplify the equations
Let's first observe each equation to see if we can simplify them.
#### Simplifying the second equation:
[tex]\[ 3y = 3x + 15 \][/tex]
We can divide each term by 3:
[tex]\[ y = x + 5 \][/tex]
Now we have the simplified version of the second equation:
[tex]\[ y = x + 5 \][/tex]
### Step 2: Substitute the simplified equation into the first equation
We can substitute \( y = x + 5 \) into the first equation \( 2y = x + 10 \).
Substituting for \( y \):
[tex]\[ 2(x + 5) = x + 10 \][/tex]
### Step 3: Solve for \( x \)
Expanding the left-hand side:
[tex]\[ 2x + 10 = x + 10 \][/tex]
Subtract \( x \) from both sides:
[tex]\[ x + 10 = 10 \][/tex]
Subtract 10 from both sides:
[tex]\[ x = 0 \][/tex]
### Step 4: Solve for \( y \)
Using the value of \( x \) that we found in the equation \( y = x + 5 \), we can find \( y \).
Substituting \( x = 0 \):
[tex]\[ y = 0 + 5 \][/tex]
[tex]\[ y = 5 \][/tex]
### Solution
The solution to the system of equations is:
[tex]\[ x = 0 \][/tex]
[tex]\[ y = 5 \][/tex]
So the values that satisfy the given system of equations are:
[tex]\[ (x, y) = (0, 5) \][/tex]
