solve the following system of equations graphically on the set of axes below.\n$y = \\frac{3}{5}x + 1$\n$x +…

Explanation:

Step1: Analyze the first equation

The first equation is ( y = \frac{3}{5}x + 1 ), which is in slope - intercept form ((y=mx + b)) where the slope (m=\frac{3}{5}) and the y - intercept (b = 1). To graph this line, we can start by plotting the y - intercept at the point ((0,1)). Then, using the slope, from the point ((0,1)), we can move up 3 units and to the right 5 units (since slope=(\frac{\text{rise}}{\text{run}}=\frac{3}{5})) to get another point, say ((5,4)).

Step2: Analyze the second equation

The second equation is (x + y=-7). We can rewrite it in slope - intercept form by solving for (y): (y=-x - 7) Here, the slope (m=- 1) and the y - intercept (b=-7). To graph this line, we plot the y - intercept at the point ((0,-7)). Then, using the slope (which is (-1=\frac{- 1}{1})), from the point ((0,-7)), we can move down 1 unit and to the right 1 unit (or up 1 unit and to the left 1 unit) to get another point, for example, ((1,-8)) or ((-1,-6)).

Step3: Find the intersection point

The solution of the system of equations is the point of intersection of the two lines. We can also solve the system algebraically to find the intersection point and then verify it graphically. We have the system: (\begin{cases}y=\frac{3}{5}x + 1\y=-x - 7\end{cases}) Set the two expressions for (y) equal to each other: (\frac{3}{5}x+1=-x - 7) Multiply through by 5 to clear the fraction: (3x + 5=-5x-35) Add (5x) to both sides: (3x + 5x+5=-5x+5x-35) (8x + 5=-35) Subtract 5 from both sides: (8x+5 - 5=-35 - 5) (8x=-40) Divide both sides by 8: (x = - 5) Substitute (x=-5) into (y=-x - 7): (y=-(-5)-7=5 - 7=-2)

Answer:

The solution of the system of equations is (x=-5,y = - 2) or the point ((-5,-2))