Questions: X=3y+7 3x-2y=7

X=3y+7 3x-2y=7
Transcript text: X=3y+7 3x-2y=7
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Solution

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Solution Steps

To solve the system of linear equations, we can use substitution or elimination. Here, we will use substitution. First, solve the first equation for \( y \) in terms of \( x \). Then, substitute this expression for \( y \) into the second equation to solve for \( x \). Finally, use the value of \( x \) to find \( y \).

Step 1: Solve the First Equation for \( y \)

Given the equation \( x = 3y + 7 \), we solve for \( y \):

\[ y = \frac{x - 7}{3} \]

Step 2: Substitute into the Second Equation

Substitute \( y = \frac{x - 7}{3} \) into the second equation \( 3x - 2y = 7 \):

\[ 3x - 2\left(\frac{x - 7}{3}\right) = 7 \]

Step 3: Simplify and Solve for \( x \)

Simplify the equation:

\[ 3x - \frac{2x - 14}{3} = 7 \]

Multiply through by 3 to eliminate the fraction:

\[ 9x - (2x - 14) = 21 \]

Simplify further:

\[ 9x - 2x + 14 = 21 \]

\[ 7x = 7 \]

Solve for \( x \):

\[ x = 1 \]

Step 4: Substitute Back to Find \( y \)

Substitute \( x = 1 \) back into the expression for \( y \):

\[ y = \frac{1 - 7}{3} = \frac{-6}{3} = -2 \]

Final Answer

The solution to the system of equations is:

\[ \boxed{x = 1, \, y = -2} \]

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