Question

a system of two equations is shown.
$\

$$\begin{cases} y = x + 1 \\\\ y = -2x + 4 \\end{cases}$$

$
determine the solution of the system of equations.
enter the correct answers in the boxes.
show hints

Explanation:

Step1: Set equations equal (substitution)

Since $y = x+1$ and $y=-2x+4$, set $x+1 = -2x+4$.

Step2: Solve for $x$

$x + 2x = 4 - 1$
$3x = 3$
$x = \frac{3}{3} = 1$

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

Substitute $x=1$ into $y = x+1$:
$y = 1 + 1 = 2$

Answer:

$x=1$, $y=2$ (or the ordered pair $(1, 2)$)