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{:[-5x+y=6],[-10 x+8y=18]:}

$\newline$ $\begin{array}{l} -5 x+y=6 \\ -10 x+8 y=18 \end{array}$

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Sine and cosine of complementary angles

Full solution

Q.

\newline

\begin{array}{l} -5 x+y=6 \\ -10 x+8 y=18 \end{array}

Given System of Equations: We are given the system of equations: $\newline$ $\begin{align*} -5x + y &= 6 \\ -10x + 8y &= 18 \end{align*}$ $\newline$ We will solve this system by substitution. First, we need to solve one of the equations for one variable. Let's solve the first equation for y. $\newline$ $y = 6 + 5x$
Solve for y: Now that we have y expressed in terms of x, we can substitute this expression into the second equation to find x. $\newline$ Substitute $y = 6 + 5x$ into the second equation: $\newline$ $-10x + 8(6 + 5x) = 18$
Substitute into Second Equation: Distribute the $8$ into the parentheses and simplify the equation. $\newline$ $-10x + 48 + 40x = 18$ $\newline$ Combine like terms: $\newline$ $30x + 48 = 18$
Simplify and Combine Terms: Subtract $48$ from both sides to isolate the term with x. $\newline$ $30x = 18 - 48$ $\newline$ $30x = -30$
Isolate x Term: Divide both sides by $30$ to solve for x. $\newline$ $x = \frac{-30}{30}$ $\newline$ $x = -1$
Solve for x: Now that we have the value of x, we can substitute it back into the expression we found for y in Step $1$ to find the value of y. $\newline$ $y = 6 + 5(-1)$ $\newline$ $y = 6 - 5$ $\newline$ $y = 1$

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