Question

Which graph represents the solution to the given system? y= -3x+4 and y=2x-1

Answer 1

It’s probably the graph where the lines intersect at (1,1). What you have to do is...
-3x+4=2x-1
+3x +3x
4=5x-1
+1 +1
5=5x
5/5=5x/5
1=x

After you find the x, you have to find the y by plugging in the x to the equation
y= -3(1) +4
y= -3+4
y=1

You can check it with the other equation go make sure.

Answer 2

The solution to the given system is a graph of the plane xy with just one point graphed in the coordinates (1, 1).

Explanation:

We have two equations of y depending of x, to know the solution of the system we can simply equalize both expressions of y, and clear the value of x. Then we evaluate both equations in that value of x to obtain the solution for the system.

So, first we calculate

`-3x+4=2x-1 \Leftrightarrow 5x=5 \Leftrightarrow x=1`

Now, we evaluate

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

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

Therefore, the solution is the point (1, 1) in the plane xy.