Questions: Use substitution to solve the system. x = 3y - 17 5x + 3y = -13 x= y=

Transcript text: Use substitution to solve the system. \[ \begin{aligned} x & =3 y-17 \\ 5 x+3 y & =-13 \end{aligned} \] \[ x= \] \[ y= \]

Solution

Solution Steps

Step 1: Substitute \( x \) from the first equation into the second equation

Given the first equation: \[ x = 3y - 17 \] Substitute \( x = 3y - 17 \) into the second equation: \[ 5x + 3y = -13 \] This becomes: \[ 5(3y - 17) + 3y = -13 \]

Step 2: Expand and simplify the equation

Expand the equation: \[ 15y - 85 + 3y = -13 \] Combine like terms: \[ 18y - 85 = -13 \]

Step 3: Solve for \( y \)

Add 85 to both sides: \[ 18y = 72 \] Divide both sides by 18: \[ y = 4 \]

Step 4: Substitute \( y = 4 \) back into the first equation to solve for \( x \)

Substitute \( y = 4 \) into \( x = 3y - 17 \): \[ x = 3(4) - 17 \] Simplify: \[ x = 12 - 17 \] \[ x = -5 \]

Final Answer

\[ x = \boxed{-5} \] \[ y = \boxed{4} \]

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