Question

\\2y - x = 0\\
\\x = y + 7\\
if \\((x, y)\\) satisfies the given system of equations, what is the value of \\(x\\)?

Explanation:

Express x in terms of y

We are given a system of two linear equations:

$$ 2y - x = 0 $$

$$ x = y + 7 $$

The second equation already expresses \(x\) directly in terms of \(y\).

Substitute x into the first equation

We substitute the expression for \(x\) from the second equation, \(x = y + 7\), into the first equation:

$$ 2y - (y + 7) = 0 $$

Solve for y

We simplify the equation to find the value of \(y\):

$$ 2y - y - 7 = 0 $$

$$ y - 7 = 0 $$

$$ y = 7 $$

Calculate the value of x

Now we substitute \(y = 7\) back into the second equation to find \(x\):

$$ x = 7 + 7 $$

$$ x = 14 $$

Answer:

If \((x, y)\) satisfies the given system of equations, what is the value of \(x\)? <blank>14</blank>