To determine if the ordered pair [tex]\((-5, 2)\)[/tex] satisfies the given equation [tex]\(2x + 4y = 6\)[/tex], follow these steps:
1. Substitute the values of the ordered pair into the equation. The ordered pair [tex]\((-5, 2)\)[/tex] means [tex]\(x = -5\)[/tex] and [tex]\(y = 2\)[/tex].
2. Calculate the left side of the equation using these values:
[tex]\[
2x + 4y = 2(-5) + 4(2)
\][/tex]
3. Simplify the expression:
[tex]\[
2(-5) + 4(2) = -10 + 8 = -2
\][/tex]
4. Compare the resulting value from the left side of the equation to the right side of the equation. The right side of the equation is 6.
So, the left side of the equation is [tex]\(-2\)[/tex], and the right side is 6. Since [tex]\(-2 \neq 6\)[/tex], the ordered pair [tex]\((-5, 2)\)[/tex] does not satisfy the equation [tex]\(2x + 4y = 6\)[/tex].
Hence, the conclusion is:
The ordered pair [tex]\((-5, 2)\)[/tex] does not satisfy the given equation [tex]\(2x + 4y = 6\)[/tex].
