Math Problem Statement

Vad ska du multiplicera den andra ekvationen med för att x-termerna ska "försvinna" vid additionen? Givet ekvationssystemet: 3x + 2y = 65 och x - 5y = -1.

Solution

The problemWe asks are given the following system of what equations to multiply:

the second equation1 by. so that the3 \(x x +- 2termsy = cancel out when 65 the two equations ) are2 added. .Letx5y=1. Let x - 5y = -1

’s analyze the system:

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terms cancel2 out when the equations. are added together.

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.#### To Result make: theseYou terms should cancel multiply, the multiply second the equation second by equation ( by - (3 - \3).

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When added, the xx-terms cancel out.

Would you like me to continue solving the system of equations? Here are some related questions:

  1. What happens when you add these two equations after cancellation?
  2. Can we solve for yy once the xx-terms are eliminated?
  3. How do you check the solution to ensure it satisfies both equations?
  4. Could a different multiplier also eliminate yy instead of xx?
  5. How do elimination and substitution methods compare in solving systems of equations?

Tip: Always ensure coefficients are exact opposites before adding to eliminate variables.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Elimination Method

Formulas

Ax + By = C
Elimination: Coefficients must be opposites

Theorems

Addition Property of Equality

Suitable Grade Level

Grades 8-10