Question

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a system of linear equations is given by these equations:
\\3y - 2x = -9\\
\\y = -2x + 5\\

the solution to this system is ( , ).

Explanation:

⚡ Using: introduction to systems of equations · 🆕 New: solving systems by substitution
Replace a variable with an equivalent expression

Step 1: Substitute the expression for \(y\)

Since the second equation gives \(y = -2x + 5\), substitute this expression for \(y\) in the first equation:

$$ 3(-2x + 5) - 2x = -9 $$

Step 2: Solve for \(x\)

Distribute the \(3\) and simplify the equation to find the value of \(x\):

$$ -6x + 15 - 2x = -9 $$

Combine like terms:

$$ -8x + 15 = -9 $$

Subtract \(15\) from both sides:

$$ -8x = -24 $$

Divide by \(-8\):

$$ x = 3 $$

Step 3: Solve for \(y\)

Substitute \(x = 3\) back into the equation for \(y\):

$$ y = -2(3) + 5 $$

$$ y = -6 + 5 $$

$$ y = -1 $$

Answer:

(3, -1)