Solve the system of equations

Question

(a) symbolically, (b) graphically, (c) and numerically

3x+y=6

x-y=2

There are different methods for solving a system linear equations symbolically. Here we will use elimination method.

What is the first step in the elimination method?

(a) Solve the first equation for y, then substitute the resulting expression for y in the second equation.

(b) Solve both equations for y.

(c) Write both equations in the form Ax+By=C

(d) Solve both equations for x

(Which letter is it?)

 

Answer 1

The first step is D: solve both equations for x.

This can be done by simply adding the equations. The Ys cancel out.

(3x + y = 6) + (x - y = 2) --> 3x + x + y - y = 4x = 8

x = 8/4 = 2

Now you plug in x into either equation.

x - y = 2 - y = 2 --> y = 2 - 2 = 0

3(2) + y = 6 + y = 6 --> y = 6 - 6 = 0