[tex]1. \(-4x + 2y = -3\)[/tex]
[tex]2. \(x - 5y = 2\)[/tex]
Step 1: Solve for one variable in terms of the other using Equation 2
[tex]\[ x - 5y = 2 \][/tex]
Solve for \( x \):
[tex]\[ x = 2 + 5y \][/tex]
Step 2: Substitute \(x\) into Equation 1
Now substitute \( x = 2 + 5y \) into Equation 1:
[tex]\[ -4(2 + 5y) + 2y = -3 \][/tex]
Step 3: Simplify and solve for \( y \)
[tex]\[ -8 - 20y + 2y = -3 \][/tex]
Combine like terms:
[tex]\[ -8 - 18y = -3 \][/tex]
Add 8 to both sides:
[tex]\[ -18y = 5 \][/tex]
Divide by -18:
[tex]\[ y = \frac{5}{-18} \][/tex]
[tex]\[ y = -\frac{5}{18} \][/tex]
Step 4: Substitute \(y\) back into the expression for \(x\)
Substitute \( y = -\frac{5}{18} \) back into the equation \( x = 2 + 5y \):
[tex]\[ x = 2 + 5\left(-\frac{5}{18}\right) \][/tex]
[tex]\[ x = 2 - \frac{25}{18} \][/tex]
Express 2 as a fraction to combine:
[tex]\[ x = \frac{36}{18} - \frac{25}{18} \][/tex]
[tex]\[ x = \frac{11}{18} \][/tex]
Step 5: Calculate \( 3x + 3y \)
We need to find \( 3x + 3y \):
[tex]\[ 3x + 3y = 3 \left( \frac{11}{18} \right) + 3 \left( -\frac{5}{18} \right) \][/tex]
Combine the fractions:
[tex]\[ 3x + 3y = \frac{33}{18} - \frac{15}{18} \][/tex]
[tex]\[ 3x + 3y = \frac{18}{18} \][/tex]
[tex]\[ 3x + 3y = 1 \][/tex]
So, the answer is 1.
