Question

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

Answer 1

ANSWER

(4, -1)

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,

$\frac{5}{2}x-10=0$

Add 10 to both sides of the equation,

$\begin{gathered} \frac{5}{2}x-10+10=0+10 \\ \frac{5}{2}x=10 \end{gathered}$

Multiply both sides by 2,

$\begin{gathered} 2\cdot\frac{5}{2}x=2\cdot10 \\ 5x=20 \end{gathered}$

And divide both sides by 5,

$\begin{gathered} \frac{5x}{5}=\frac{20}{5} \\ x=4 \end{gathered}$

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)