Question

Solve the system of equationsy = 2x - 9 y= - 1/2x + 1

Answer 1

(4, -1)

Step-by-step explanation

To solve this system, we can use the method of elimination. Subtract the second equation from the first,

Then, solve this equation for x,

`(5)/(2)x-10=0`

Add 10 to both sides of the equation,

`\begin{gathered} (5)/(2)x-10+10=0+10 \\ (5)/(2)x=10 \end{gathered}`

Multiply both sides by 2,

`\begin{gathered} 2\cdot(5)/(2)x=2\cdot10 \\ 5x=20 \end{gathered}`

And divide both sides by 5,

`\begin{gathered} (5x)/(5)=(20)/(5) \\ x=4 \end{gathered}`

Now, knowing that x = 4, replace its value into either of the equations from the system to find the value of y,

`y=2x-9=2\cdot4-9=8-9=-1`

The value of y = -1. Hence, the solution is the point (4, -1)