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{:[2(2x-1)-(y-4)=11],[3(1-x)-2(y-3)=-7]:}

$5$ . Solve. $\newline$ $\begin{array}{l} 2(2 x-1)-(y-4)=11 \\ 3(1-x)-2(y-3)=-7 \end{array}$

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Solve linear inequalities

Full solution

Q.

5

. Solve.

\newline

\begin{array}{l} 2(2 x-1)-(y-4)=11 \\ 3(1-x)-2(y-3)=-7 \end{array}

Expand and Simplify: First, we will expand the equations to simplify them. $\newline$ For the first equation: $2(2x - 1) - (y - 4) = 11$ $\newline$ Expand and simplify: $\newline$ $4x - 2 - y + 4 = 11$ $\newline$ $4x - y + 2 = 11$ $\newline$ Now, isolate the terms involving variables: $\newline$ $4x - y = 11 - 2$ $\newline$ $4x - y = 9$
Isolate Variables: For the second equation: $3(1 - x) - 2(y - 3) = -7$ Expand and simplify: $3 - 3x - 2y + 6 = -7$ $-3x - 2y + 9 = -7$ Now, isolate the terms involving variables: $-3x - 2y = -7 - 9$ $-3x - 2y = -16$
Expand and Simplify: Now we have a system of two equations: $\newline$ $4x - y = 9$ $\newline$ $-3x - 2y = -16$ $\newline$ We will use the method of substitution or elimination to solve this system. Let's use elimination to eliminate one of the variables. $\newline$ To eliminate $y$ , we can multiply the first equation by $2$ : $\newline$ $2(4x - y) = 2(9)$ $\newline$ $8x - 2y = 18$
Isolate Variables: Now we have the modified system of equations: $\newline$ $8x - 2y = 18$ $\newline$ $-3x - 2y = -16$ $\newline$ We will add these two equations to eliminate $y$ : $\newline$ $(8x - 2y) + (-3x - 2y) = 18 + (-16)$ $\newline$ $8x - 3x - 2y - 2y = 18 - 16$ $\newline$ $5x - 4y = 2$ $\newline$ This is incorrect; we should have eliminated $y$ , but we ended up with an equation that still contains $y$ . Let's go back and correct this mistake.

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