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Solve the system of equations.
{:[-2x+9y=11],[-5x+2y=-34]:}
x = ◻
y = ◻

Solve the system of equations. $\newline$ $\begin{array}{l}-2 x+9 y=11 \\ -5 x+2 y=-34\end{array}$ $\newline$ $x = \square$ $\newline$ $y = \square$

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Write and solve inverse variation equations

Full solution

Q. Solve the system of equations.

\newline

\begin{array}{l}-2 x+9 y=11 \\ -5 x+2 y=-34\end{array}

\newline

x = \square

\newline

y = \square

Write Equations: Write down the system of equations. $\newline$ The system of equations is given by: $\newline$ $-2x + 9y = 11$ $\newline$ $-5x + 2y = -34$ $\newline$ We will use the method of substitution or elimination to solve for $x$ and $y$ .
Multiply Equations: Multiply the first equation by $5$ and the second equation by $2$ to make the coefficients of $x$ in both equations equal in magnitude. $\newline$ Multiplying the first equation by $5$ : $\newline$ $-2x \times 5 + 9y \times 5 = 11 \times 5$ $\newline$ $-10x + 45y = 55$ $\newline$ Multiplying the second equation by $2$ : $\newline$ $-5x \times 2 + 2y \times 2 = -34 \times 2$ $\newline$ $-10x + 4y = -68$
Add Equations: Add the two new equations together to eliminate $x$ . Adding the equations $-10x + 45y = 55$ and $-10x + 4y = -68$ : $(-10x + 45y) + (-10x + 4y) = 55 + (-68)$ $-20x + 49y = -13$ This step is incorrect because we should have subtracted one equation from the other to eliminate $x$ , not added them together.

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