To solve the given system of equations using substitution and identify the correct solution, follow these steps:
Step 1: Solve the first equation for [tex]\( x \)[/tex]
The first equation is:
[tex]\[ 4x = 16 \][/tex]
To isolate [tex]\( x \)[/tex], divide both sides of the equation by 4:
[tex]\[ x = \frac{16}{4} \][/tex]
[tex]\[ x = 4 \][/tex]
Step 2: Substitute the value of [tex]\( x \)[/tex] into the second equation
The second equation is:
[tex]\[ x + y = 2 \][/tex]
Substitute [tex]\( x = 4 \)[/tex]:
[tex]\[ 4 + y = 2 \][/tex]
Step 3: Solve for [tex]\( y \)[/tex]
Subtract 4 from both sides of the equation:
[tex]\[ y = 2 - 4 \][/tex]
[tex]\[ y = -2 \][/tex]
Step 4: Identify the solution
The solution to the system of equations is the ordered pair [tex]\((x, y)\)[/tex], which is:
[tex]\[ (4, -2) \][/tex]
Step 5: Match the solution with the given options
The given options are:
1. [tex]\((-2, 4)\)[/tex]
2. [tex]\((8, -6)\)[/tex]
3. [tex]\((-4, 6)\)[/tex]
4. [tex]\((12, -10)\)[/tex]
5. [tex]\((4, -2)\)[/tex]
From the options above, option 5, [tex]\((4, -2)\)[/tex], matches our solution.
Therefore, the correct solution is [tex]\((4, -2)\)[/tex], and it corresponds to option 5.
