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

Expand and Simplify: First, we will expand the equations to simplify them. For the first equation: 2(2x - 1) - (y - 4) = 11 Expand and simplify: 4x - 2 - y + 4 = 11 4x - y + 2 = 11 Now, isolate the terms involving variables: 4x - y = 11 - 2 4x - y = 9Isolate 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 = -16Expand and Simplify: Now we have a system of two equations: 4x - y = 9 -3x - 2y = -16 We will use the method of substitution or elimination to solve this system. Let's use elimination to eliminate one of the variables. To eliminate y, we can multiply the first equation by 2: 2(4x - y) = 2(9) 8x - 2y = 18Isolate Variables: Now we have the modified system of equations: 8x - 2y = 18 -3x - 2y = -16 We will add these two equations to eliminate y: (8x - 2y) + (-3x - 2y) = 18 + (-16) 8x - 3x - 2y - 2y = 18 - 16 5x - 4y = 2 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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{:[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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Algebra 2

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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.