Question 1187243
here's the graph.


<img src = "http://theo.x10hosting.com/2021/110407.jpg" >



the intersection point is at (x,y) = (12,19).


that means y = 19 when x = 12.


if you solve algebraically, you should get the same answer.


algebraically, you would do the following:


the two equatons that need to be solved simultaneously are:


y=-5/3x-1
y=x+7


since they are both equal to y, then 5/3 * x - 1 must be equal to x + 7.


you get:


5/3 * x - 1 = x + 7


subtract x from both sides of the equation and add 1 to both sides of the equation t0 get:


5/3 * x - x = 7 + 1


multiply both sides of this equation by 3 to get:


5 * x - 3 * x = 3 * (7 + 1)


combine like terms and simplify to get:


2*x = 24.


solve for x to get:


x = 24/2 = 12.


replace x in both original equations to get:


y=-5/3x-1 becomes y = 5/3 * 12 - 1 = 20 - 1 = 19.
y=x+7 becomes y = 12 + 7 = 19.


the value of x is 12 in both equations and the value of y = 19 in both equations.


both equations have been solved simultaneously by the value of x = 12 and y = 19.


the graphical solution provided the same answer.


that's because x = 12 when y = 19 is common to both equations which means it's also common to both lines on the graph created by those equations.