Question

use the drawing tool(s) to form the correct answers on the provided answer space. giles is making tacos for dinner and bought some beef and chicken. at the store, he bought twice as much beef as chicken. the chicken costs $1.85 per pound, and the beef costs $3.70 per pound. before sales tax, giles spent a total of $12.95 on beef and chicken. the system of equations below represent the pounds of chicken, x, and pounds of beef, y, that giles purchased. y = 2x 1.85x + 3.7y = 12.95 part a: use the ray tool to graph the system of equations on the coordinate plane. part b: use the point tool to select the approximate pounds of beef giles purchased.

Explanation:

Step1: Solve the system of equations

We have the system:
\[

$$\begin{cases} y = 2x \\ 1.85x + 3.7y = 12.95 \end{cases}$$

\]
Substitute \(y = 2x\) into the second equation:
\[
1.85x + 3.7(2x) = 12.95
\]

Step2: Simplify and solve for \(x\)

First, calculate \(3.7(2x)=7.4x\), so the equation becomes:
\[
1.85x + 7.4x = 12.95
\]
Combine like terms:
\[
9.25x = 12.95
\]
Divide both sides by \(9.25\):
\[
x=\frac{12.95}{9.25} = 1.4
\]

Step3: Find \(y\)

Since \(y = 2x\), substitute \(x = 1.4\):
\[
y = 2\times1.4 = 2.8
\]

Answer:

For Part B, the approximate pounds of beef Giles purchased is \(2.8\) pounds. So we would use the point tool to select the point \((1.4, 2.8)\) on the coordinate plane (where the x - coordinate is pounds of chicken and y - coordinate is pounds of beef). For Part A, to graph \(y = 2x\), we can start at the origin \((0,0)\) and use the ray tool to draw a line with a slope of 2 (e.g., passing through \((1,2)\), \((2,4)\) etc.). To graph \(1.85x+3.7y = 12.95\), we can rewrite it in slope - intercept form \(y=-\frac{1.85}{3.7}x+\frac{12.95}{3.7}\), which simplifies to \(y = - 0.5x+3.5\). We can start at the y - intercept \((0,3.5)\) and use the ray tool to draw a line with a slope of - 0.5 (e.g., passing through \((2,2.5)\), \((4,1.5)\) etc.). The intersection point of these two rays is \((1.4,2.8)\), which is the solution for the system.