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Solve the given system of equations:

[tex]\[
\begin{array}{l}
2y = -x + 9 \\
3x - 6y = -15
\end{array}
\][/tex]

The solution to the system is ([tex]\(\square\)[/tex], [tex]\(\square\)[/tex]).

Sagot :

GinnyAnswer
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]
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