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Solve the system of equations. $10y - 11x = -4$ and $-2y + 3x = 4$

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Solve a system of equations in three variables using substitution

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Q. Solve the system of equations.

10y - 11x = -4

and

-2y + 3x = 4

Set up equations: Set up the system of equations to be solved. $\newline$ We have the following two equations: $\newline$ $1$ ) $10y - 11x = -4$ $\newline$ $2$ ) $-2y + 3x = 4$
Multiply second equation: Multiply the second equation by $5$ to make the coefficient of $y$ in both equations the same (but opposite in sign). $\newline$ $5 \times (-2y + 3x) = 5 \times 4$ $\newline$ This gives us: $\newline$ $-10y + 15x = 20$
Add equations to eliminate $y$ : Add the new equation from Step $2$ to the first equation to eliminate $y$ . $(10y - 11x) + (-10y + 15x) = -4 + 20$ This simplifies to: $4x = 16$
Solve for x: Solve for x. $\newline$ $4x = 16$ $\newline$ $x = \frac{16}{4}$ $\newline$ $x = 4$
Substitute $x$ into equation: Substitute the value of $x$ back into one of the original equations to solve for $y$ . We'll use the second equation: $-2y + 3x = 4$ .
$-2y + 3(4) = 4$
$-2y + 12 = 4$
Solve for y: Solve for y. $\newline$ $-2y = 4 - 12$ $\newline$ $-2y = -8$ $\newline$ $y = -8 / -2$ $\newline$ $y = 4$

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