Question 594529
y = 5x + 11
y = -4x - 7
There are many methods to solve this. When deciding which method to use, it is helpful to know how to pick a method which will be easy. For the substitution method, look for a variable that is already "solved for" or can easily be "solved for". ("Solved for" means the variable is by itself on one side of the equation.)<br>
Since the "y" is already "solved for" in the first equation (and the second, for that matter), the Substitution method will probably be easiest method.<br>
With this method, after you have solved for one of the variables in one of the equations, you substitute for that variable in the other equation. Since y is already "solved for" in the first equation we can substitute for y in the other equation. Replacing the y in the second equation with the 5x + 11 from the first equation we get:
5x + 11 = -4x - 7<br>
We now have an equation of one variable. This is relatively easy to solve. Adding 4x to each side we get:
9x + 11 = -7
Subtracting 11 from each side we get:
9x = -18
Dividing by 9 we get:
x = -2<br>
It is tempting to stop here. But we need both the x and the y of the solution. The next step is to use the value we got for x and substitute it into one of the original equations and solve for y. Substituting the -2 for x in the first equation we get:
y = 5(-2) + 11
Simplifying...
y = -10 + 11
y = 1<br>
So the solution to this system is the point (-2, 1)