Question

use the substitution method to solve the system of equations. choose the correct ordered pair.
2x - y = 10
2x - 2y = 4
a. (2, -2)
b. (8, 6)
c. (2, -1)
d. (7, 4)

Explanation:

Step1: Solve first equation for y

From \(2x - y = 10\), we can rewrite it as \(y = 2x - 10\).

Step2: Substitute y into second equation

Substitute \(y = 2x - 10\) into \(2x - 2y = 4\). So we have \(2x - 2(2x - 10)=4\).
Expand the equation: \(2x - 4x + 20 = 4\).
Combine like terms: \(-2x + 20 = 4\).
Subtract 20 from both sides: \(-2x = 4 - 20=-16\).
Divide both sides by -2: \(x=\frac{-16}{-2} = 8\).

Step3: Find y using x = 8

Substitute \(x = 8\) into \(y = 2x - 10\). Then \(y=2\times8 - 10=16 - 10 = 6\).

Answer:

B. \((8, 6)\)