Question

use the substitution method to solve the system of equations. choose the correct ordered pair. 14x - 2y = 78 2x - 2y = 6 a. (7,3) b. (7,4) c. (6,3) d. (6,4)

Explanation:

Step1: Solve the second equation for \(2y\)

From \(2x - 2y = 6\), we can rewrite it as \(2y = 2x - 6\).

Step2: Substitute \(2y\) into the first equation

The first equation is \(14x - 2y = 78\). Substitute \(2y = 2x - 6\) into it:
\(14x - (2x - 6) = 78\)
Simplify the left side: \(14x - 2x + 6 = 78\)
Combine like terms: \(12x + 6 = 78\)
Subtract 6 from both sides: \(12x = 78 - 6 = 72\)
Divide both sides by 12: \(x = \frac{72}{12} = 6\)

Step3: Find the value of \(y\)

Now that we know \(x = 6\), substitute \(x = 6\) into \(2y = 2x - 6\):
\(2y = 2\times6 - 6 = 12 - 6 = 6\)
Divide both sides by 2: \(y = \frac{6}{2} = 3\)

Answer:

C. \((6, 3)\)