Question 305455
To graph the equation -6x + 10y = -60, you have to solve for y to get:


y = (6x -60)/10


To graph the equation 7x - 6y = -42, you have to solve for y to get:


y = (7x + 42)/6


The graph looks like this:


{{{graph(600,600,-30,10,-30,10,(6x-60)/10,(7x+42)/6)}}}


The intersection of these lines looks like it is around (-23,-20).


To find the intersection, solve these equations simultaneously.


The equations are:


-6x + 10y = -60
7x - 6y = -42


Multiply the first equation by 7 and the second equation  by 6 to get:


-42x + 70y = -420
42x - 36y = -252


Add these 2 equations together to get:


34y = -672


Divide both sides of this equation by 34 to get:


y = -19.76470588


Substitute for y in the first original equation to get:


-6x + 10y = -60 becomes:


-6x - 197.6470588 = -60


Add 197.6470588 to both sides of this equation to get:


-6x = 137.6470588


Divide both sides of this equation by -6 to get:


x = -22.94117647


You have an intersection at:


x = -22.94117647
y = -19.76470588


The graph confirms that in the detail it is possible to get from the graph.


The easiest way to estimate is to use a piece of paper and line up the horizontal side of the paper with the bottom of your computer screen and then see what the x-value is by sliding the paper sideways.


You can see what the y-value is by lining up the paper with the y-axis and then sliding the paper up and down until you can estimate what the y-value of the instersection is.