Question

Choose the graph that best represents the solution to the system of equations.

y=-x
y=x-1

Answer 1

First, rearrange the equations:

`x + y = 0`

`- x + y = - 1`

Then, do equation 1 minus equation 2 to cancel y:

`x - - x = 2x`

`0 - - 1 = 1`

`2x = 1`

`x = (1)/(2)`

Substitute x to find y:

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

So the point of intersection is (1/2, -1/2), which is represented by graph 1.

Answer 2

Given system of equations,

y = - x ------(1)

y = x - 1 ------(2),

From equation (1) and (2),

-x = x - 1

-x - x = -1

-2x = -1

`\implies x = (1)/(2)`

Again from equation (1),

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

Thus, the intersection point of the lines (1) and (2), is
`((1)/(2), -(1)/(2))`

Hence, the below graph represents the solution to the system of equations.