Question

Find the solution to the system of equations. Write the solution as an ordered pair

5x + 2y =6
4x -8y= 0

Answer 1

Answer:The solutions are (1, 1/2)

Explanation:

5x + 2y = 6 - - - - - - - - 1

4x - 8y= 0 - - - - - - - - - - - 2

We would apply the elimination method to solve the set of simultaneous equations.

We would eliminate x by multiplying equation 1 by 4 and equation 2 by 5. It becomes

20x + 8y = 24

20x - 40y= 0

Subtracting both equations, it becomes

8y - - 40y = 24 - 0

48y = 24

Dividing the left hand side and the right hand side of the equation by 48, it becomes

48y/48 = 24/48

y = 1/2

Substituting y = 1/2 into equation 2, it becomes

4x - 8 × 1/2= 0

4x - 4 = 0

4x = 4

x = 4/4 = 1

Answer 2

(1, 1/2)

Explanation:

Divide the second equation by 4 and add 2y:

x -2y = 0

x = 2y

Now, you can substitute for either x or 2y in the first equation.

Substituting for x:

5(2y) +2y = 6

12y = 6 . . . . . collect terms

y = 6/12 = 1/2 . . . . divide by 12

Substituting for 2y:

5x +x = 6

6x = 6 . . . . . collect terms

x = 1 . . . . . . . divide by 6

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The solution is ...

(x, y) = (1, 1/2)