Question

solve the system of equations by graphing.
\

$$\begin{cases} 5x + y = 6 \\\\ y = 5 \\end{cases}$$

use the graphing tool to graph the system.
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graph

Explanation:

Step1: Rewrite the first equation in slope - intercept form

The first equation is \(5x + y=6\). We can rewrite it in the slope - intercept form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept) by solving for \(y\).
Subtract \(5x\) from both sides of the equation: \(y=-5x + 6\).
The slope of this line is \(m=-5\) and the y - intercept is \(b = 6\). To graph this line, we can start by plotting the y - intercept at \((0,6)\). Then, using the slope (rise over run), since the slope is \(-5=\frac{-5}{1}\), we can go down 5 units and to the right 1 unit from the y - intercept to get another point (for example, \((1,1)\)), and then draw the line through these points.

Step2: Graph the second equation

The second equation is \(y = 5\). This is a horizontal line (since the equation is in the form \(y = k\), where \(k = 5\)) that passes through all points with a y - coordinate of 5. So we can plot the points \((0,5)\), \((1,5)\), \((2,5)\), etc., and draw a horizontal line through these points.

Step3: Find the intersection point

To solve the system of equations \(

$$\begin{cases}5x + y=6\\y = 5\end{cases}$$

\), we can substitute \(y = 5\) into the first equation.
Substitute \(y = 5\) into \(5x + y=6\):
\(5x+5 = 6\)
Subtract 5 from both sides: \(5x=6 - 5=1\)
Divide both sides by 5: \(x=\frac{1}{5}=0.2\)

So the solution to the system of equations is the point of intersection of the two lines, which is \((\frac{1}{5},5)\) or \((0.2,5)\).

Answer:

The solution to the system of equations is \(\boldsymbol{(0.2,5)}\) (or \(\boldsymbol{(\frac{1}{5},5)}\)).