How do you solve the following system of equations?: #4x – 5y = 14 , 7x + 3y=10#?
There are a few ways to solve these two equations. One way is by graphing the two and seeing where they intersect. Another way is by substitution, where you isolate one variable in one of the equations, then plugging in that value in place of the variable.
My favorite way is by elimination. That is where you set up the equations just like how you'd do solve a normal subtraction/addition problem, such as this :
Then you set it up so that two variables have the same coefficient so they can be added or subtracted to equal zero. After that you're left with 1 variable, which can be easily solved for.
Once you have the value for that variable, you plug it into one of the original equations and solve for the other variable. After you have both variables, you check your answers by plugging them into the second equation.
This might sound complicated, but we'll put into practice and go through it step by step.
First, we set it up like an addition/subtraction problem:
Now normally we'd just pick a variable to solve for, say
Now if we subtract the
Let's solve for
First we plug
Let's double check our work by plugging in our values for
That looks like this:
Congratulations! We were correct!