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$3x+6y=15, x+y=3, y=?$

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Solve equations involving like terms

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Q.

3x+6y=15, x+y=3, y=?

Identify Equations: Identify the system of equations to solve for $y$ . We have two equations: $1$ ) $3x + 6y = 15$ $2$ ) $x + y = 3$ We need to solve for $y$ .
Solve for x: Solve the second equation for x in terms of y. $\newline$ $x + y = 3$ $\newline$ Subtract y from both sides to isolate x: $\newline$ $x = 3 - y$
Substitute $x$ into $1$ st equation: Substitute the expression for $x$ from Step $2$ into the first equation. $\newline$ Replace $x$ in $3x + 6y = 15$ with the expression from Step $2$ : $\newline$ $3(3 - y) + 6y = 15$
Distribute and Simplify: Distribute $3$ into the parentheses and simplify the equation. $3(3) - 3(y) + 6y = 15$ $9 - 3y + 6y = 15$
Combine Like Terms: Combine like terms. $\newline$ $9 + 3y = 15$
Isolate y Term: Subtract $9$ from both sides to isolate the term with $y$ . $\newline$ $3y = 15 - 9$ $\newline$ $3y = 6$
Solve for y: Divide both sides by $3$ to solve for y. $\newline$ y = $\frac{6}{3}$ $\newline$ y = $2$

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