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Solve Systems of Equations by Elimination: example 5.34 · Physics Playground

Exercises Systems of equations

Example 5.34 from Elementary Algebra, 5.3 Solve Systems of Equations by Elimination

Solve Systems of Equations by Elimination: example 5.34

For each system of linear equations decide whether it would be more convenient to solve it by substitution or elimination. Explain your answer.

ⓐ ${\begin{matrix} 3 x + 8 y = 40 \\ 7 x - 4 y = −32 \end{matrix}$ ⓑ ${\begin{matrix} 5 x + 6 y = 12 \\ y = \frac{2}{3} x - 1 \end{matrix}$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. ⓐ $\begin{matrix} {\begin{matrix} 3 x + 8 y = 40 \\ 7 x - 4 y = −32 \end{matrix} \end{matrix}$
  Since both equations are in standard form, using elimination will be most convenient.
2. ⓑ $\begin{matrix} {\begin{matrix} 5 x + 6 y = 12 \\ y = \frac{2}{3} x - 1 \end{matrix} \end{matrix}$
>Since one equation is already solved for y, using substitution will be most convenient.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

For each system of linear equations, decide whether it would be more convenient to solve it by substitution or elimination. Explain your answer.

ⓐ ${\begin{matrix} 4 x - 5 y = −32 \\ 3 x + 2 y = −1 \end{matrix}$ ⓑ ${\begin{matrix} x = 2 y - 1 \\ 3 x - 5 y = - 7 \end{matrix}$

How did it go?

PreviousSolve Systems of Equations by Elimination: example 5.33 Next Solve Applications with Systems of Equations: example 5.35

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 5.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.

Solution

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