Question

2x+5y=55
9x-2y=3
solve (round to nearest hundreth)

Answer 1

To solve the system of equations:

1. \( 2x + 5y = 55 \) (Equation 1)
2. \( 9x - 2y = 3 \) (Equation 2)

We can use the substitution or elimination method. I will use the substitution method.

### Step 1: Solve Equation 1 for \( y \)

From Equation 1:

\[
5y = 55 - 2x
\]

\[
y = \frac{55 - 2x}{5}
\]

### Step 2: Substitute \( y \) in Equation 2

Now, substitute the expression for \( y \) into Equation 2:

\[
9x - 2\left(\frac{55 - 2x}{5}\right) = 3
\]

### Step 3: Simplify the equation

Multiply both sides by 5 to eliminate the fraction:

\[
5(9x) - 2(55 - 2x) = 15
\]

\[
45x - 110 + 4x = 15
\]

Combine like terms:

\[
49x - 110 = 15
\]

### Step 4: Solve for \( x \)

Add 110 to both sides:

\[
49x = 125
\]

Now, divide by 49:

\[
x = \frac{125}{49} \approx 2.55 \text{ (rounded to nearest hundredth)}
\]

### Step 5: Substitute \( x \) back to find \( y \)

Now substitute \( x \) back into the equation for \( y \):

\[
y = \frac{55 - 2\left(\frac{125}{49}\right)}{5}
\]

Calculate \( 2 \times \frac{125}{49} \):

\[
2 \times \frac{125}{49} = \frac{250}{49}
\]

Now substitute back into the equation for \( y \):

\[
y = \frac{55 - \frac{250}{49}}{5}
\]

Converting 55 to a fraction:

\[
55 = \frac{2695}{49}
\]

Now we have:

\[
y = \frac{\frac{2695 - 250}{49}}{5}
\]

Calculate \( 2695 - 250 = 2445 \):

\[
y = \frac{\frac{2445}{49}}{5} = \frac{2445}{245}
\]

Now we divide:

\[
y = \frac{2445 \div 245}{1} \approx 9.98 \text{ (rounded to nearest hundredth)}
\]

### Final Result

The solution to the system of equations is approximately:

\[
x \approx 2.55, \quad y \approx 9.98
\]