Math Problem Statement
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.
’s analyze the system:
\The[
question\begin asks{aligned}
what1 you. should \quad multiply 3 thex second + equation by2 soy &= that 65 \ the -
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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: The1. How do you modified determine second equation what to multiply each becomes equation by to eliminate: a variable? \2. Why does[ eliminating one variable- make solving3(x the - system easier5? y3. Can) = you -3(- eliminate1 ) y \ instead ofim in this + system ?15y If = yes,3 how ? ]
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###
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.Always \quad -3 checkx the signs of + the coefficients 15 carefullyy when &= eliminating variables to3
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When added, the -terms cancel out.
Would you like me to continue solving the system of equations? Here are some related questions:
- What happens when you add these two equations after cancellation?
- Can we solve for once the -terms are eliminated?
- How do you check the solution to ensure it satisfies both equations?
- Could a different multiplier also eliminate instead of ?
- 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