Given the system of equations:
x + y = 13 (Equation 1)
1/2x + y = 10 (Equation 2)
To find the solution to the system, you can follow the steps below:
Step 1: Isolate y in Equation 1.
[tex]\begin{gathered} x+y=13 \\ y=13-x \end{gathered}[/tex]Step 2: Substitute y by (13 - x) in Equation 2.
[tex]\begin{gathered} \frac{1}{2}x+y=10 \\ \frac{1}{2}x+13-x=10 \end{gathered}[/tex]Step 3: Isolate x.
To do it, first, add -13 to each of the equality.
[tex]\begin{gathered} \frac{1}{2}x+13-x-13=10-13 \\ \frac{1}{2}x-x=-3 \end{gathered}[/tex]Put all x together using the same denominator:
[tex]\begin{gathered} \frac{1x-2x}{2}=-3 \\ -\frac{x}{2}=-3 \end{gathered}[/tex]Multiply both sides by (-2)
[tex]\begin{gathered} -\frac{x}{2}=-3 \\ -\frac{x}{2}\cdot(-2)=-3\cdot(-2) \\ \frac{2}{2}x=6 \\ x=6 \end{gathered}[/tex]Step 4: Find y using Equation 1.
Since you found x, you can substitute it in Equation 1 and find y.
[tex]\begin{gathered} x+y=13 \\ 6+y=13 \end{gathered}[/tex]Subtract 6 from each side to isolate y.
[tex]\begin{gathered} 6+y-6=13-6 \\ y=7 \end{gathered}[/tex]Answer:
x = 6; y = 7
Alternative B. (6, 7)