Question

find the solution of the system of equations.

$-2x + 2y = 6$

$7x + 4y = 23$

Explanation:

Step1: Simplify the first equation

Divide the first equation \(-2x + 2y = 6\) by 2, we get \(-x + y = 3\), which can be rewritten as \(y = x + 3\).

Step2: Substitute \(y\) into the second equation

Substitute \(y = x + 3\) into the second equation \(7x + 4y = 23\), we have \(7x + 4(x + 3) = 23\).
Expand the equation: \(7x + 4x + 12 = 23\).
Combine like terms: \(11x + 12 = 23\).
Subtract 12 from both sides: \(11x = 23 - 12 = 11\).
Divide both sides by 11: \(x = 1\).

Step3: Find the value of \(y\)

Substitute \(x = 1\) into \(y = x + 3\), we get \(y = 1 + 3 = 4\).

Answer:

The solution of the system is \(x = 1\), \(y = 4\) (or in ordered pair form \((1, 4)\))