Question

which point is a solution to the system of linear equations?
y = -x + 1
3x - y = 3
options:
(\frac{3}{2}, -\frac{1}{2})
(1, 0)
(-\frac{1}{2}, \frac{3}{2})
(0, 1)

Explanation:

Step1: Substitute $y=-x+1$ into the second equation

Substitute $y$ in $3x - y = 3$:
$$3x - (-x + 1) = 3$$

Step2: Simplify and solve for $x$

Expand and combine like terms:
$$3x + x - 1 = 3$$
$$4x - 1 = 3$$
$$4x = 4$$
$$x = 1$$

Step3: Find $y$ using $x=1$

Substitute $x=1$ into $y=-x+1$:
$$y = -1 + 1 = 0$$

Step4: Verify the solution

Check $(1,0)$ in $3x - y = 3$:
$$3(1) - 0 = 3$$
$$3 = 3$$
The point satisfies both equations.

Answer:

(1, 0)