Questions: 4x + 3y = -4 Y = 3x - 10

Transcript text: 4 x+3 y=-4 Y=3 x-10

Solution

Step 1: Substitute the Expression for \( y \)

Given the system of equations:

\[ \begin{array}{l} 4x + 3y = -4 \\ y = 3x - 10 \end{array} \]

We substitute the expression for \( y \) from the second equation into the first equation:

\[ 4x + 3(3x - 10) = -4 \]

Step 2: Simplify the Equation

Distribute the 3 in the equation:

\[ 4x + 9x - 30 = -4 \]

Combine like terms:

\[ 13x - 30 = -4 \]

Step 3: Solve for \( x \)

Add 30 to both sides of the equation:

\[ 13x = 26 \]

Divide both sides by 13:

\[ x = 2 \]

Step 4: Solve for \( y \)

Substitute \( x = 2 \) back into the equation for \( y \):

\[ y = 3(2) - 10 \]

Simplify:

\[ y = 6 - 10 = -4 \]

The solution to the system of equations is:

\[ \boxed{x = 2} \]

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

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