Questions: Which shows the correct way to input the value of x into the first equation? -2 x + 4 y = 15 x = -1/2 3 x + y = 2 -2 - 1/2 + 4 y = 15 -2(-1/2) + 4 y = 15

Transcript text: Which shows the correct way to input the value of $x$ into the first equation? \[ \begin{aligned} -2 x+4 y & =15 \quad x=-\frac{1}{2} \\ 3 x+y & =2 \\ -2-\frac{1}{2}+4 y & =15 \end{aligned} \] $-2\left(-\frac{1}{2}\right)+4 y=15$

Solution

Solution Steps

Step 1: Substitute the value of $ x $ into the first equation

The given value of $ x $ is $ x = -\frac{1}{2} $. Substitute this value into the first equation: \[ -2x + 4y = 15 \] Substituting $ x = -\frac{1}{2} $: \[ -2\left(-\frac{1}{2}\right) + 4y = 15 \]

Step 2: Simplify the equation

Simplify the left-hand side of the equation: \[ -2\left(-\frac{1}{2}\right) = 1 \] So the equation becomes: \[ 1 + 4y = 15 \]

Step 3: Solve for $ y $

Subtract 1 from both sides of the equation: \[ 4y = 15 - 1 \] \[ 4y = 14 \] Divide both sides by 4: \[ y = \frac{14}{4} = \frac{7}{2} \]