Question

Question 3 (1 point) Solve the system of equation using the elimination method. Your answer has to be an ordered pair (x, y) x - 2y = 11 2x + y = 19 Blank 1:

Answer 1

Given:

x - 2y = 11

2x + y = 19

To solve using elimination method, we have:

• Step 1:

Multiply equation 1 by 2, then multiply equation 2 by 1.

x - 2y = 11 ....................x2

2x + y = 19...................x1

2x - 4y = 22

2x + y = 19

• Step 2:

Now, subtract both equations:

`\begin{gathered} 2x-4y=22 \\ -2x\text{ +y = 19} \\ _(----------) \\ \text{ -5y = }3 \end{gathered}`

• Divide both sides by -5:

Replace y with -3/5 in any of the equations to find x.

Let's take equation 2:

`\begin{gathered} 2x\text{ -}(3)/(5)=19 \\ \end{gathered}`

Multiply through by 5 to eliminate the fraction:

`\begin{gathered} 2x(5)-(3)/(5)\ast5=19(5) \\ \\ 10x-3=95 \end{gathered}`

Add 3 to both sides:

`\begin{gathered} 10x-3+3=95+3 \\ \\ 10x\text{ = 98} \end{gathered}`

Divide both sides by 10:

`\begin{gathered} (10x)/(10)=(98)/(10) \\ \\ x\text{ =}(49)/(5) \end{gathered}`
`x\text{ = }(49)/(5),\text{ and y=-}(3)/(5)`

ANSWER:

`\text{(}(49)/(5),\text{ -}(3)/(5))`