Question

find the solution of the system of equations. \

$$\begin{cases} 3x + 4y = 19 \\\\ -3x + 4y = 13 \\end{cases}$$

show your work here \\( x = \\) \\( y = \\) check

Explanation:

Step1: Eliminate \(x\) by adding equations

Add the two equations \(3x + 4y = 19\) and \(-3x + 4y = 13\):
\((3x - 3x) + (4y + 4y) = 19 + 13\)
Simplify: \(8y = 32\)

Step2: Solve for \(y\)

Divide both sides by 8:
\(y = \frac{32}{8} = 4\)

Step3: Substitute \(y = 4\) to find \(x\)

Substitute \(y = 4\) into \(3x + 4y = 19\):
\(3x + 4(4) = 19\)
Simplify: \(3x + 16 = 19\)
Subtract 16: \(3x = 3\)
Divide by 3: \(x = 1\)

Answer:

\(x = 1\), \(y = 4\)