Answer :
To solve the given system of equations:
[tex]\[ \begin{array}{l} 2.5 y + 3 x = 27 \\ 5 x - 2.5 y = 5 \end{array} \][/tex]
### Step 1: Adding the Two Equations
First, we add the two equations together:
[tex]\[ (2.5 y + 3 x) + (5 x - 2.5 y) = 27 + 5 \][/tex]
Let's combine like terms:
[tex]\[ 2.5 y - 2.5 y + 3 x + 5 x = 32 \][/tex]
[tex]\[ 0 + 8 x = 32 \][/tex]
[tex]\[ 8 x = 32 \][/tex]
So, the resulting equation from adding the two equations is:
[tex]\[ 8 x = 32 \][/tex]
### Step 2: Solving for [tex]\( x \)[/tex]
Now, solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{32}{8} = 4 \][/tex]
### Step 3: Solving for [tex]\( y \)[/tex]
Next, substitute [tex]\( x = 4 \)[/tex] back into one of the original equations to find [tex]\( y \)[/tex]. Let's use the first equation:
[tex]\[ 2.5 y + 3(4) = 27 \][/tex]
[tex]\[ 2.5 y + 12 = 27 \][/tex]
Subtract 12 from both sides:
[tex]\[ 2.5 y = 27 - 12 \][/tex]
[tex]\[ 2.5 y = 15 \][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{15}{2.5} = 6 \][/tex]
### Final Solution
Thus, the resulting equation from adding the two equations is:
[tex]\[ 8 x = 32 \][/tex]
And the solution to the system of equations is:
[tex]\[ x = 4 \quad \text{and} \quad y = 6 \][/tex]
[tex]\[ \begin{array}{l} 2.5 y + 3 x = 27 \\ 5 x - 2.5 y = 5 \end{array} \][/tex]
### Step 1: Adding the Two Equations
First, we add the two equations together:
[tex]\[ (2.5 y + 3 x) + (5 x - 2.5 y) = 27 + 5 \][/tex]
Let's combine like terms:
[tex]\[ 2.5 y - 2.5 y + 3 x + 5 x = 32 \][/tex]
[tex]\[ 0 + 8 x = 32 \][/tex]
[tex]\[ 8 x = 32 \][/tex]
So, the resulting equation from adding the two equations is:
[tex]\[ 8 x = 32 \][/tex]
### Step 2: Solving for [tex]\( x \)[/tex]
Now, solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{32}{8} = 4 \][/tex]
### Step 3: Solving for [tex]\( y \)[/tex]
Next, substitute [tex]\( x = 4 \)[/tex] back into one of the original equations to find [tex]\( y \)[/tex]. Let's use the first equation:
[tex]\[ 2.5 y + 3(4) = 27 \][/tex]
[tex]\[ 2.5 y + 12 = 27 \][/tex]
Subtract 12 from both sides:
[tex]\[ 2.5 y = 27 - 12 \][/tex]
[tex]\[ 2.5 y = 15 \][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{15}{2.5} = 6 \][/tex]
### Final Solution
Thus, the resulting equation from adding the two equations is:
[tex]\[ 8 x = 32 \][/tex]
And the solution to the system of equations is:
[tex]\[ x = 4 \quad \text{and} \quad y = 6 \][/tex]
