Math Problem Statement

What is the x-value in the solution to this system of equations? (Use the elimination method). Given equations: 8x + y = -16 and -3x + y = -5.

Solution

To solve the system of equations using the elimination method:

  1. Given the equations:

    8x + y &= -16 \\ -3x + y &= -5 \end{align*}$$
  2. Subtract the second equation from the first to eliminate yy: (8x+y)(3x+y)=16(5)(8x + y) - (-3x + y) = -16 - (-5) 8x+y+3xy=16+58x + y + 3x - y = -16 + 5 11x=1111x = -11

  3. Solve for xx: x=1111=1x = \frac{-11}{11} = -1

So, the xx-value in the solution to this system of equations is 1-1. The correct answer is D. 1-1.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
System of Equations
Elimination Method

Formulas

Elimination method: Combine equations to eliminate one variable

Theorems

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Suitable Grade Level

Grades 8-10