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\
(\square, \square)

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other: \( x + 1 = -2x + 4 \)

Step2: Solve for \( x \)

Add \( 2x \) to both sides: \( x + 2x + 1 = 4 \) which simplifies to \( 3x + 1 = 4 \). Then subtract 1 from both sides: \( 3x = 4 - 1 \) so \( 3x = 3 \). Divide both sides by 3: \( x = \frac{3}{3} = 1 \)

Step3: Find \( y \) using \( x = 1 \)

Substitute \( x = 1 \) into \( y = x + 1 \): \( y = 1 + 1 = 2 \)

Answer:

(1, 2)