Question

Solve the following system of equations using the elimination method. 5x – 5y = 10 6x – 4y = 4

Answer 1

To solve the system of equations using elimination, we first manipulate the equations to have the same coefficient for y, then subtract one equation from the other to eliminate y, solve for x, and substitute x back into one of the original equations to solve for y, getting the solution x = -2 and y = -4.

Step-by-step explanation:

Solving the System of Equations Using Elimination

To solve the given system of linear equations using the elimination method:

1. The system of equations is:
   
2. Multiply the first equation by 4 and the second equation by 5 to get the coefficients of y to be the same:
   
3. The new system of equations will be:
   
4. Subtract the first new equation from the second to eliminate y:
   
5. Divide by 10 to find x:
   
6. Substitute x = -2 into one of the original equations to solve for y. For example, using the first original equation:
   
7. Now we have the solution for the system: x = -2 and y = -4.
8. Check the answer by substituting x and y into both original equations to ensure they satisfy both equations.
   

Answer 2

x=-2,y=-4

Step-by-step explanation:

By dividing to lowest terms

5x – 5y = 10= x-y=2.......(1)

6x – 4y = 4=3x-2y=2........(2)

By elimination method

Multiply equation (1) by 3 so as to correspond with equation (2)

3(x-y)=3(2)

3x-3y=6..........(3)

Multiply equation (2) by 1 so as to correspond with equation (1)

1(3x-2y)=1(2)

3x-2y=2..........(4)

Then equation (3)-equation (4)

(3x-3y=6)

-

(3x-2y=2)

__________

-y=4

y=-4

Substitute y=-4 into equation(1)

x-(-4)=2

x+4=2

x=-2

Therefore x=-2,y=-4