To find the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] that satisfy the given system of linear equations [tex]\( x - y = 2 \)[/tex] and [tex]\( x + y = 4 \)[/tex], we follow these steps:
1. Write the Equations:
We are given the system of equations:
[tex]\[
x - y = 2 \quad \text{(Equation 1)}
\][/tex]
[tex]\[
x + y = 4 \quad \text{(Equation 2)}
\][/tex]
2. Add the Equations:
Adding Equation 1 and Equation 2 helps eliminate [tex]\(y\)[/tex]:
[tex]\[
(x - y) + (x + y) = 2 + 4
\][/tex]
Simplifying, we get:
[tex]\[
2x = 6
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Divide both sides by 2:
[tex]\[
x = 3
\][/tex]
4. Substitute [tex]\(x\)[/tex] into One of the Original Equations:
Substitute [tex]\(x = 3\)[/tex] into Equation 1 to find [tex]\(y\)[/tex]:
[tex]\[
3 - y = 2
\][/tex]
Solving for [tex]\(y\)[/tex], we get:
[tex]\[
y = 3 - 2
\][/tex]
[tex]\[
y = 1
\][/tex]
Thus, the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are [tex]\(a = 3\)[/tex] and [tex]\(b = 1\)[/tex].
Therefore, the correct option is:
(c) 3 and 1
