Question

\begin{aligned} &y=2x +1 \\\\ &x-y=-3 \end{aligned} ​ y=2x+1 x−y=−3 ​ Is (2,5)(2,5)left parenthesis, 2, comma, 5, right parenthesis a solution of the system?

Answer 1

Yes

Explanation:

Given the system of equations

`\begin{aligned} &y=2x +1 \\\\ &x-y=-3 \end{aligned}`

We want to determine if (2,5) is a solution of the system.

We can do this by substitution of the given point into the equations and see if it holds.

Given (x,y)=(2,5), x=2, y=5

In the first equation

y=2x+1

5=2(2)+1

5=5

Therefore, the point (2,5) satisfies the first equation.

In the second equation

`x-y=2-5=-3`

Since our result (-3) is equal to the Right Hand Side, the point also satisfies the second equation.

Therefore, (2,5) is a solution of the system.