2 variable systems. Solve using any method

Question

2=-2y+4x

0=-y+2x-1

Answer 1

2 variable systems. Solve using any method

2=-2y+4x

0=-y+2x-1

Use substitution method.

0 = -y + 2x - 1

+y = +y - y + 2x -1

y = 2x - 1

2 = -2(2x-1) +4x

2 = -4x +2 +4x

x=0 2=2 reflective property

2=-2y+4x

2=-2y +4(0)

2=-2y

2/-2 = ( -2/-2) y

-1 = y

Answer 2

When you have multiple equations and multiple variables to solve for, you must first make sure you don't have more variables than equations (or else it is unsolvable). Here we have two variables, so we need at least 2 equations, which we have.

You can solve by substitution (rearranging one equation to isolate a variable, and then plugging in that expression into the other equation) or elimination (adding the equations together to eliminate one variable).

Let's try substitution:

2=-2y+4x equation (1)

0=-y+2x-1 equation (2)

If we add +y to both sides of equation 2, we have isolated one of our variables.

2=-2y+4x equation (1)

y=2x-1 equation (2)

Now we can plug in (2x-1) into equation (1) for y.

2 = -2(2x-1) + 4x

Now we have an equation with only one variable, so we can solve for x.

2 = -4x +2 + 4x

uh-oh, looks like our 4x's cancel out and we are left with 2 = 2. Because this is true for all values of x and y, there are infinitely many solutions to this system of equations.

The solution to a system of equations is the point at which the two lines cross. If there are infinitely many solutions, that means the two equations are of the same line. Let's put both equations in matching form to see if they are the same:

2=-2y+4x equation (1)

0=-y+2x-1 equation (2)

Divide equation 1 by 2

1=-y+2x

Subtract 1 from both sides

0 = -y + 2x -1

Now we can see that equation (1) perfectly matches equation (2), so they are the same line and have infinitely many solutions.