Question

Solve the system of equations by using elimination. Write the solution as an ordered pair.6x + 8y = 85x + 4y = 3

Answer 1

Given:

6x + 8y = 8

5x + 4y = 3

Let's solve the system of equations using elimination method.

Take the followings steps:

Step 1:

Multiply each equation by any value that makes the coefficient of y opposite.

Multiply equation 2 by (-2):

6x + 8y = 8

-2(5x + 4y = 3)

6x + 8y = 8

-10x - 8y = -6

Add the two equations:

6x + 8y = 8

+ -10x - 8y = -6

_______________

-4x + 0 = 2

-4x = 2

Divide both sides by -4:

`\begin{gathered} (-4x)/(-4)=(2)/(-4) \\ \\ x=-(1)/(2) \end{gathered}`

Substitute -½ for x in either of the equations.

Take equation 1:

`\begin{gathered} 6x+8y=8 \\ \\ 6(-(1)/(2))+8y=8 \\ \\ -3+8y=8 \end{gathered}`

Add 3 to both sides:

`\begin{gathered} 3-3+8y=8+3 \\ \\ 8y=11 \end{gathered}`

Divide both sides by 8:

`\begin{gathered} (8y)/(8)=(11)/(8) \\ \\ y=(11)/(8) \end{gathered}`

Thus, we have the solutions:

`(x,y)\Longrightarrow(-(1)/(2),(11)/(8))`

ANSWER:

`(-(1)/(2),(11)/(8))`