Question

Choose the correct graph of the given system of equations.

y − 2x = −1
x + 3y = 4

Answer 1

I believe it'd the one in the middle because if you plug in the values (1,1) both equations are true.
Plug x=1 and y=1 in equations:
LHS = 1 - 2*1 = 1-2 = -1 = RHS
LHS = 1 + 3*1 = 4 = RHS
So it's the graph in the middle.

Answer 2

The 2nd attachment contains the correct plot for the given equation.

Solution-

We can predict which graph corresponds to the given system, by either plotting the equations or by calculating the solution to the system and then comparing with the given options.

Solving the equation,

`y-2x=-1 \ and \ x+3y = 4`

we can get the solution.

`x+3y = 4`

`\Rightarrow x=4-3y`

Putting it in the first equation,

`y-2(4-3y)=-1`

`\Rightarrow y-8+6y=-1`

`\Rightarrow 7y=7`

`\Rightarrow y=1`

Then putting the value of y=1, in the second equation,

`\Rightarrow x=4-3(1)=1`

`\therefore \ (1, 1) \ is \ the \ only \ solution`