Question

is $x = 4$, $y = \frac{1}{2}$ a solution of the given system of equations?
\

$$\begin{cases} 2x - 4y = 6\\\\ \\frac{1}{2}x - 3y = \\frac{1}{2} \\end{cases}$$

is the first equation satisfied?
\bigcirc no
\bigcirc yes

is the second equation satisfied?
\bigcirc no
\bigcirc yes

as a result, is $x = 4$, $y = \frac{1}{2}$ a solution of the given system of equations?
\bigcirc no
\bigcirc yes

Explanation:

Step1: Check first equation

Substitute \(x = 4\), \(y=\frac{1}{2}\) into \(2x - 4y\):
\(2(4)-4(\frac{1}{2}) = 8 - 2=6\), which equals the right - hand side of the first equation (\(6\)). So the first equation is satisfied.

Step2: Check second equation

Substitute \(x = 4\), \(y=\frac{1}{2}\) into \(\frac{1}{2}x-3y\):
\(\frac{1}{2}(4)-3(\frac{1}{2})=2-\frac{3}{2}=\frac{4 - 3}{2}=\frac{1}{2}\), which equals the right - hand side of the second equation (\(\frac{1}{2}\)). So the second equation is satisfied.

Step3: Determine the solution of the system

Since both equations are satisfied when \(x = 4\) and \(y=\frac{1}{2}\), \(x = 4\), \(y=\frac{1}{2}\) is a solution of the system.

Answer:

s:

• Is the first equation satisfied? Yes
• Is the second equation satisfied? Yes
• As a result, is \(x = 4,y=\frac{1}{2}\) a solution of the given system of equations? Yes