Question

How many solutions does the system of equations below have? y=3x+4 y+6x=3x

Answer 1

Answer:

x = -$\frac{2}{3}$

y = 2

Step-by-step explanation:

The process of elimination is a method of solving a system of equations. One must first manipulate one of the equations such that one of the variables shared between the two equations has the inverse coefficient of the same variable in the other equation. Therefore, when one adds the equations, the variable cancels. One can solve for the variable using inverse operations, and then backsolve to find the value of the first variable.

When given the following system:

y = 3x + 4

y + 6x = 3x

Use inverse operations so that both equations are solve for one variable,

y = 3x + 4

y = -3x

Add the systems so that one of the variables (x) cancels, this process is called the process of elimination;

y = 3x + 4

y = -3x

_________

2y = 4

Inverse operations,

2y = 4

y = 2

Now backsolve, find the value of (x) by substituting the value of (y) into the equation:

y = -3x

2 = -3x

x = -$\frac{2}{3}$