Answer :
Certainly! Let’s solve the given system of equations step-by-step using the substitution method.
The system of equations is:
[tex]\[ \begin{array}{l} 2y = -x + 9 \\ 3x - 6y = -15 \end{array} \][/tex]
Step 1: Solve the first equation for [tex]\( y \)[/tex]
Starting with the first equation:
[tex]\[ 2y = -x + 9 \][/tex]
Divide both sides by 2 to isolate [tex]\( y \)[/tex]:
[tex]\[ y = \frac{-x + 9}{2} \][/tex]
Step 2: Substitute the expression for [tex]\( y \)[/tex] into the second equation
Now, take the expression we found for [tex]\( y \)[/tex] and substitute it into the second equation:
[tex]\[ 3x - 6\left(\frac{-x + 9}{2}\right) = -15 \][/tex]
Distribute [tex]\(-6\)[/tex] inside the parentheses:
[tex]\[ 3x - 3(-x + 9) = -15 \][/tex]
Simplify the expression inside the parentheses:
[tex]\[ 3x + 3x - 27 = -15 \][/tex]
Combine like terms:
[tex]\[ 6x - 27 = -15 \][/tex]
Step 3: Solve for [tex]\( x \)[/tex]
Add 27 to both sides to solve for [tex]\( x \)[/tex]:
[tex]\[ 6x - 27 + 27 = -15 + 27 \][/tex]
Simplify both sides:
[tex]\[ 6x = 12 \][/tex]
Divide by 6:
[tex]\[ x = 2 \][/tex]
Step 4: Substitute the value of [tex]\( x \)[/tex] back into the expression for [tex]\( y \)[/tex]
Now substitute [tex]\( x = 2 \)[/tex] back into the equation we found for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{-2 + 9}{2} \][/tex]
Simplify the numerator:
[tex]\[ y = \frac{7}{2} \][/tex]
[tex]\[ y = 3.5 \][/tex]
So the solution to the system of equations is:
[tex]\[ (2, 3.5) \][/tex]
The system of equations is:
[tex]\[ \begin{array}{l} 2y = -x + 9 \\ 3x - 6y = -15 \end{array} \][/tex]
Step 1: Solve the first equation for [tex]\( y \)[/tex]
Starting with the first equation:
[tex]\[ 2y = -x + 9 \][/tex]
Divide both sides by 2 to isolate [tex]\( y \)[/tex]:
[tex]\[ y = \frac{-x + 9}{2} \][/tex]
Step 2: Substitute the expression for [tex]\( y \)[/tex] into the second equation
Now, take the expression we found for [tex]\( y \)[/tex] and substitute it into the second equation:
[tex]\[ 3x - 6\left(\frac{-x + 9}{2}\right) = -15 \][/tex]
Distribute [tex]\(-6\)[/tex] inside the parentheses:
[tex]\[ 3x - 3(-x + 9) = -15 \][/tex]
Simplify the expression inside the parentheses:
[tex]\[ 3x + 3x - 27 = -15 \][/tex]
Combine like terms:
[tex]\[ 6x - 27 = -15 \][/tex]
Step 3: Solve for [tex]\( x \)[/tex]
Add 27 to both sides to solve for [tex]\( x \)[/tex]:
[tex]\[ 6x - 27 + 27 = -15 + 27 \][/tex]
Simplify both sides:
[tex]\[ 6x = 12 \][/tex]
Divide by 6:
[tex]\[ x = 2 \][/tex]
Step 4: Substitute the value of [tex]\( x \)[/tex] back into the expression for [tex]\( y \)[/tex]
Now substitute [tex]\( x = 2 \)[/tex] back into the equation we found for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{-2 + 9}{2} \][/tex]
Simplify the numerator:
[tex]\[ y = \frac{7}{2} \][/tex]
[tex]\[ y = 3.5 \][/tex]
So the solution to the system of equations is:
[tex]\[ (2, 3.5) \][/tex]