Question

1. solve for \\(x\\) and \\(y\\) using elimination method.

\\-4 + y = -10\\
\\4x - 3y = 14\\

Explanation:

Identify the system of equations

We are given a system of linear equations to solve:

1. \(-4 + y = -10\)
2. \(4x - 3y = 14\)

Solve for y from the first equation

The first equation contains only the variable \(y\). We can solve for \(y\) directly by adding \(4\) to both sides:

$$ y = -10 + 4 $$

$$ y = -6 $$

Substitute y into the second equation

Now we substitute \(y = -6\) into the second equation to solve for \(x\):

$$ 4x - 3(-6) = 14 $$

$$ 4x + 18 = 14 $$

Solve for x

Subtract \(18\) from both sides of the equation:

$$ 4x = 14 - 18 $$

$$ 4x = -4 $$

Divide by \(4\):

$$ x = -1 $$

Verify the solution

We check our values \(x = -1\) and \(y = -6\) in both original equations:

• First equation: \(-4 + (-6) = -10\) (True)
• Second equation: \(4(-1) - 3(-6) = -4 + 18 = 14\) (True)

Answer:

\(x = -1\), \(y = -6\)