Get expert insights and community-driven knowledge on IDNLearn.com. Ask anything and receive thorough, reliable answers from our community of experienced professionals.
Sagot :
To determine which ordered pair is the solution to the system of equations
[tex]\[ \left\{\begin{array}{l} x + 2y = -8 \\ y = \frac{1}{2}x - 2 \end{array}\right., \][/tex]
we need to verify which pair satisfies both equations.
Let's analyze each pair one by one.
### Pair [tex]\((-2, -1)\)[/tex]
1. Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = -1\)[/tex] into the first equation [tex]\(x + 2y = -8\)[/tex]:
[tex]\[ -2 + 2(-1) = -2 - 2 = -4 \quad (\text{not } -8) \][/tex]
Hence, this pair does not satisfy the first equation.
### Pair [tex]\((-2, -3)\)[/tex]
1. Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = -3\)[/tex] into the first equation [tex]\(x + 2y = -8\)[/tex]:
[tex]\[ -2 + 2(-3) = -2 - 6 = -8 \quad (\text{correct}) \][/tex]
2. Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = -3\)[/tex] into the second equation [tex]\(y = \frac{1}{2}x - 2\)[/tex]:
[tex]\[ -3 = \frac{1}{2}(-2) - 2 = -1 - 2 = -3 \quad (\text{correct}) \][/tex]
This pair satisfies both equations.
### Pair [tex]\((-6, -5)\)[/tex]
1. Substitute [tex]\(x = -6\)[/tex] and [tex]\(y = -5\)[/tex] into the first equation [tex]\(x + 2y = -8\)[/tex]:
[tex]\[ -6 + 2(-5) = -6 - 10 = -16 \quad (\text{not } -8) \][/tex]
Hence, this pair does not satisfy the first equation.
### Pair [tex]\((-4, -4)\)[/tex]
1. Substitute [tex]\(x = -4\)[/tex] and [tex]\(y = -4\)[/tex] into the first equation [tex]\(x + 2y = -8\)[/tex]:
[tex]\[ -4 + 2(-4) = -4 - 8 = -12 \quad (\text{not } -8) \][/tex]
Hence, this pair does not satisfy the first equation.
Based on the above evaluations, the only ordered pair that satisfies both equations is:
[tex]\[ (-2, -3) \][/tex]
Thus, the solution to the system of equations is [tex]\(\boxed{(-2, -3)}\)[/tex].
[tex]\[ \left\{\begin{array}{l} x + 2y = -8 \\ y = \frac{1}{2}x - 2 \end{array}\right., \][/tex]
we need to verify which pair satisfies both equations.
Let's analyze each pair one by one.
### Pair [tex]\((-2, -1)\)[/tex]
1. Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = -1\)[/tex] into the first equation [tex]\(x + 2y = -8\)[/tex]:
[tex]\[ -2 + 2(-1) = -2 - 2 = -4 \quad (\text{not } -8) \][/tex]
Hence, this pair does not satisfy the first equation.
### Pair [tex]\((-2, -3)\)[/tex]
1. Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = -3\)[/tex] into the first equation [tex]\(x + 2y = -8\)[/tex]:
[tex]\[ -2 + 2(-3) = -2 - 6 = -8 \quad (\text{correct}) \][/tex]
2. Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = -3\)[/tex] into the second equation [tex]\(y = \frac{1}{2}x - 2\)[/tex]:
[tex]\[ -3 = \frac{1}{2}(-2) - 2 = -1 - 2 = -3 \quad (\text{correct}) \][/tex]
This pair satisfies both equations.
### Pair [tex]\((-6, -5)\)[/tex]
1. Substitute [tex]\(x = -6\)[/tex] and [tex]\(y = -5\)[/tex] into the first equation [tex]\(x + 2y = -8\)[/tex]:
[tex]\[ -6 + 2(-5) = -6 - 10 = -16 \quad (\text{not } -8) \][/tex]
Hence, this pair does not satisfy the first equation.
### Pair [tex]\((-4, -4)\)[/tex]
1. Substitute [tex]\(x = -4\)[/tex] and [tex]\(y = -4\)[/tex] into the first equation [tex]\(x + 2y = -8\)[/tex]:
[tex]\[ -4 + 2(-4) = -4 - 8 = -12 \quad (\text{not } -8) \][/tex]
Hence, this pair does not satisfy the first equation.
Based on the above evaluations, the only ordered pair that satisfies both equations is:
[tex]\[ (-2, -3) \][/tex]
Thus, the solution to the system of equations is [tex]\(\boxed{(-2, -3)}\)[/tex].
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.