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Chapter 7: Problem 1

Use the linear system below. $$-x+y=5 \quad \text { Equation } 1$$ $$\frac{1}{2} x+y=8 \quad \text { Equation } 2$$ Which equation would you choose to solve for y? Why?

Short Answer

Expert verified
Equation 1 (\(-x + y = 5\)) would be chosen to solve for y because it can be simplified to y = x + 5 in just one step.

Step by step solution

01

Evaluate equations

Examine both equations. Equation 1 is \(-x + y = 5\) and equation 2 is \(0.5x + y = 8\). In equation 1, we can simply isolate y by moving x to the other side of the equal sign.
02

Solving Equation 1

To isolate y in the first equation, add x to both sides to get: \(y = x + 5\).
03

Judging the ease of solving

Equation 1 was simplified to y in just one step, which was fairly easy. To isolate y in Equation 2, first subtract \(0.5x\) from both sides to get: \(y = 8 - 0.5x\). This requires more steps, and also involves dealing with a fraction, which can complicate calculations. Therefore, Equation 1 is a better choice to solve for y, because its transformation is simpler.

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Most popular questions from this chapter

Use the following information. A carpenter is buying supplies for a job. The carpenter needs 4 sheets of oak paneling and 2 sheets of shower tileboard. The carpenter pays 99.62 dollars for these supplies. For the next job the carpenter buys 12 sheets of oak paneling and 6 sheets of shower tileboard and pays 298.86 dollars. If the carpenter later spends a total of 139.69 dollars for 1 sheet of shower tileboard and 8 sheets of oak paneling, could you find how much 1 sheet of oak paneling costs? Explain.

Graph the function. $$ f(x)=2 x+3 $$

Use the linear system below. $$\begin{array}{l} y=x+3 \\ y=2 x+3 \end{array}$$ Solve the linear system using substitution. What does the solution mean?

You know how to solve the equation \(\frac{1}{2} x+2=\frac{3}{2} x-12\) algebraically. This equation can also be solved graphically by solving the linear system. $$ \begin{aligned} &y=\frac{1}{2} x+2\\\ &y=\frac{3}{2} x-12 \end{aligned} $$ a. Explain how the linear system is related to the original equation. b. Solve the system graphically. c. Check that the \(x\) -coordinate from part (b) satisfies the original equation \(\frac{1}{2} x+2=\frac{3}{2} x-12\) by substituting the \(x\) -coordinate for \(x\)

Use the linear system below. $$\begin{array}{l} y=x+3 \\ y=2 x+3 \end{array}$$ Graph the system. Explain what the graph shows.
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