Solving equations by using elimination?

Question

 

do anyone know ?
x-2y=4
y=x-2
 

1/3x +y=1
-4+y=1

y=x
2y=x+4

-2/7x - 4/3y=8
4/7x+8/3y=-16

Answer 1

x - 2y = 4

y = x - 2

Add  -y  to each side

-y + y = x -y -2

0 = x - y - 2

Add 2 to each side

2 = x - y

There fore the equations are x - 2y = 4 and x - y = 2

x - 2y = 4     (1)

x - y = 2      (2)

Eliminate x for the above equations then -2y + y = 4-2

-y = 2

y  = -2

Multiply the each side by 2 for the (2) equation

2x - 2y = 4     (3)

Subtract from (1) and (3)

-x + 0 = 0

-x = 0

x = 0

Therefore the values of the equation is x = 0 and y = -2.

Answer 2

Elimination method.

2) The equations are and

The second equation - 4 + y  = 1

Add 4 to each side .

y  = 5 _____ (2)

Since the coefficient of the y - term in two equations is same, i can eliminate these terms by sutract equation (2) from first equation.

Write the equations in column form and add to eliminate variable y.

The resultant equation is and solve it for x.

x = - 12

Solution x = -12 and y = 5.

Answer 3

Elimination method.

3) The equations are y  = x  and 2y = x + 4

Write the equations in standard form is ax + by  = c.

- x + y = 0 _____  (1)

- x + 2y = 4 _____ (2)

Step -1

Since the coefficient of the x - term in two equations is same, i can eliminate these terms by sutract second equation  from first equation.

The resultant equation is - y = - 4 and solve for y.

Multiply each side by negative one.

y = 4

Step - 2
Subtitute the value in any one of the equations to solve other variable.

Take the equation y = x

Substitute y = 4 we get,

 x = 4

Solution x = 4 and y = 4.

Answer 4

Elimination method.

2) The equations are and

The second equation - 4 + y  = 1

Add 4 to each side .

y  = 5 _____ (2)

Since the coefficient of the y - term in two equations is same, i can eliminate these terms by sutract equation (2) from first equation.

The resultant equation is and solve it for x.

x = - 12

Solution x = -12 and y = 5.

Answer 5

4) The equations are

First equation

Multiply each side by negative 2.

Observe the two equations are same.

Since they are equal lines there infinitely many solutions.