Question

What is the value of x in the solution to the following system of linear equations

y=x-1
y=2x+1

Answer 1

Since the equations are equal to each other, let's set them up.

x-1=2x+1; let's add 1 to both sides.

x=2x+2; let's subtract 2x from both sides.

-x=2; we need x to be positive so let's divide it by -1.

x=-2

Let's see what y is and see if x is -2.

y=-2-1=-3

y=-2(-2)+1=-4+1=-3

So, x=-2 and y=-3.

Answer 2

`\left\{\begin{array}{ccc}y=x-1\\y=2x+1\end{array}\right\Rightarrow 2x+1=x-1\\\\2x+1=x-1\ \ \ \ |-1\\2x=x-2\ \ \ |-x\\x=-2\\\\\text{substitute the value of x to the first equation}\\\\y=-2-1\\y=-3\\\\\text{Answer:}\ \boxed{x=-2;\ y=-3}`