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Solve the system:

{:[x+6y=17],[-x+3y=-8]:}

Solve the system: $\newline$ $\begin{array}{c} x+6 y=17 \\ -x+3 y=-8 \end{array}$

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Sine and cosine of complementary angles

Full solution

Q. Solve the system:

\newline

\begin{array}{c} x+6 y=17 \\ -x+3 y=-8 \end{array}

Write Equations: Write down the system of equations. $\newline$ We have the following system of equations: $\newline$ $1$ ) $x + 6y = 17$ $\newline$ $2$ ) $-x + 3y = -8$
Add Equations: Add the two equations together to eliminate $x$ . $\newline$ $(1) + (2)$ gives us: $\newline$ $x + 6y - x + 3y = 17 - 8$ $\newline$ This simplifies to: $\newline$ $9y = 9$
Solve for y: Solve for y. $\newline$ Divide both sides of the equation by $9$ to isolate y: $\newline$ $\frac{9y}{9} = \frac{9}{9}$ $\newline$ $y = 1$
Substitute and Solve: Substitute the value of $y$ back into one of the original equations to solve for $x$ . Using equation ( $1$ ), $x + 6y = 17$ , we substitute $y = 1$ : $x + 6(1) = 17$ $x + 6 = 17$
Final Solution: Solve for $x$ . $\newline$ Subtract $6$ from both sides of the equation to isolate $x$ : $\newline$ $x + 6 - 6 = 17 - 6$ $\newline$ $x = 11$

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