Questions: Solve the following systems of equations for the unknown variables. Enter your answer in ( x, y ) format. 6x + 3y = 18 5x + y = 15

Transcript text: Solve the following systems of equations for the unknown variables. Enter your answer in ( $x, y$ ) format. \[ \begin{array}{l} 6 x+3 y=18 \\ 5 x+y=15 \end{array} \]

Solution

Solution Steps

Step 1: Solve the second equation for $ y $

We start with the second equation: \[ 5x + y = 15 \] Solving for $ y $: \[ y = 15 - 5x \]

Step 2: Substitute $ y $ into the first equation

Substitute $ y = 15 - 5x $ into the first equation: \[ 6x + 3(15 - 5x) = 18 \] Simplify the equation: \[ 6x + 45 - 15x = 18 \] Combine like terms: \[ -9x + 45 = 18 \]

Step 3: Solve for $ x $

Subtract 45 from both sides: \[ -9x = 18 - 45 \] \[ -9x = -27 \] Divide both sides by -9: \[ x = 3 \]

Step 4: Solve for $ y $

Substitute $ x = 3 $ back into the expression for $ y $: \[ y = 15 - 5(3) \] \[ y = 15 - 15 \] \[ y = 0 \]