Question

1. sally and ray work together on an assignment. they have broken down the work into 4 parts of the same size. sally works at 2 times the speed of ray but has 5 pieces of work to do for another subject. this problem can be represented by the following system of equations: equation 1: x + y = 4 equation 2: y = 2x - 5 6a sketch the two lines representing these equations on the graph below.

Explanation:

Step1: Analyze Equation 1 ($x + y = 4$)

This is a linear equation in two variables. To sketch it, find two points. When $x = 0$, $y = 4$ (point: $(0, 4)$). When $y = 0$, $x = 4$ (point: $(4, 0)$). Plot these two points and draw a line through them.

Step2: Analyze Equation 2 ($y = 2x - 5$)

This is in slope - intercept form ($y=mx + b$, where $m = 2$ (slope) and $b=- 5$ (y - intercept)). The y - intercept is $(0,-5)$. To find another point, use the slope. From $(0,-5)$, move up 2 units and right 1 unit (since slope is 2) to get $(1,-3)$. Plot $(0,-5)$ and $(1,-3)$ (or other points) and draw the line.

(Note: Since the graph is partially shown with some points marked, we can also check the intersection of the two lines. Solve the system

$$\begin{cases}x + y=4\\y = 2x-5\end{cases}$$

. Substitute $y = 2x - 5$ into $x + y=4$: $x+(2x - 5)=4\Rightarrow3x=9\Rightarrow x = 3$, then $y=4 - 3 = 1$. So the intersection point is $(3,1)$. We can verify if the lines pass through this point and the other calculated points.)

Answer:

(The process to sketch the lines: For $x + y = 4$, plot $(0,4)$ and $(4,0)$ and draw the line. For $y = 2x-5$, plot $(0, - 5)$ and $(1,-3)$ (or use the intersection point $(3,1)$) and draw the line. The final graph should have two lines, one for each equation, intersecting at $(3,1)$.)