Question

use the substitution method to solve the system of equations. choose the correct ordered pair.\\(3x + y = 10\\)\\(y = x - 2\\)\\(\bigcirc\\) a. \\((3, 1)\\)\\(\bigcirc\\) b. \\((2, 0)\\)\\(\bigcirc\\) c. \\((4, 2)\\)\\(\bigcirc\\) d. \\((5, 3)\\)

Explanation:

Step1: Substitute \( y = x - 2 \) into \( 3x + y = 10 \)

We replace \( y \) in the first equation with \( x - 2 \) from the second equation. So we get \( 3x+(x - 2)=10 \).

Step2: Simplify and solve for \( x \)

First, simplify the left - hand side of the equation: \( 3x+x - 2=10 \), which combines like terms to \( 4x-2 = 10 \). Then, add 2 to both sides of the equation: \( 4x-2 + 2=10 + 2 \), so \( 4x=12 \). Divide both sides by 4: \( x=\frac{12}{4}=3 \).

Step3: Find the value of \( y \)

Substitute \( x = 3 \) into the equation \( y=x - 2 \). Then \( y=3 - 2=1 \).

Answer:

A. \((3,1)\)