Question

solve the system of equations \

$$\begin{cases}4x + y = 14 \\\\ 5x - 3y = 9\\end{cases}$$

Explanation:

Step1: Solve the first equation for y

From \(4x + y = 14\), we can express \(y\) in terms of \(x\) by subtracting \(4x\) from both sides.
\(y = 14 - 4x\)

Step2: Substitute y into the second equation

Substitute \(y = 14 - 4x\) into \(5x - 3y = 9\).
\(5x - 3(14 - 4x) = 9\)

Step3: Simplify and solve for x

First, distribute the -3 in \(-3(14 - 4x)\):
\(5x - 42 + 12x = 9\)
Combine like terms:
\(17x - 42 = 9\)
Add 42 to both sides:
\(17x = 9 + 42\)
\(17x = 51\)
Divide both sides by 17:
\(x = \frac{51}{17}\)
\(x = 3\)

Step4: Substitute x back to find y

Now that we know \(x = 3\), substitute it into \(y = 14 - 4x\).
\(y = 14 - 4(3)\)
\(y = 14 - 12\)
\(y = 2\)

Answer:

The solution to the system of equations is \(x = 3\) and \(y = 2\)