Question

skill practice - standard form
b1: 2x + y = 5 and x - y = 1
solve by graphing.

Explanation:

Step1: Rewrite equations in slope - intercept form

For the equation \(2x + y=5\), we can rewrite it as \(y=- 2x + 5\). The slope \(m_1=-2\) and the y - intercept \(b_1 = 5\).
For the equation \(x - y=1\), we can rewrite it as \(y=x - 1\). The slope \(m_2 = 1\) and the y - intercept \(b_2=-1\).

Step2: Find two points for each line

For \(y=-2x + 5\):
When \(x = 0\), \(y=-2(0)+5=5\), so we have the point \((0,5)\).
When \(x = 2\), \(y=-2(2)+5=1\), so we have the point \((2,1)\).
For \(y=x - 1\):
When \(x = 0\), \(y=0 - 1=-1\), so we have the point \((0,-1)\).
When \(x = 2\), \(y=2 - 1 = 1\), so we have the point \((2,1)\).

Step3: Graph the lines

Plot the points for each line and draw the lines. The first line (from \(y=-2x + 5\)) passes through \((0,5)\) and \((2,1)\), and the second line (from \(y=x - 1\)) passes through \((0,-1)\) and \((2,1)\). The point of intersection of the two lines is the solution of the system of equations.
From the points we found, both lines pass through \((2,1)\), so the intersection point is \((2,1)\).

Answer:

The solution of the system of equations \(

$$\begin{cases}2x + y=5\\x - y=1\end{cases}$$

\) is \(x = 2,y = 1\) or the ordered pair \((2,1)\).