Question

nom :
groupe :
date :
4 cst révision chapitre 4
(la résolution algébrique d’un système d’équations)
#1. résous chacun des systèmes d’équations suivants à l’aide de la méthode de comparaison.
a)
\

$$\begin{cases} y = x + 8 \\\\ y = 5x \\end{cases}$$

couple-solution :
b)
\

$$\begin{cases} x = 10y - 19 \\\\ x = 3y - 5 \\end{cases}$$

couple-solution :

Explanation:

Part (a)

Step1: Set the two equations equal

Since both equal \( y \), we set \( x + 8 = 5x \).

Step2: Solve for \( x \)

Subtract \( x \) from both sides: \( 8 = 4x \), then divide by 4: \( x = 2 \).

Step3: Find \( y \)

Substitute \( x = 2 \) into \( y = 5x \), so \( y = 5\times2 = 10 \).

Step1: Set the two equations equal

Since both equal \( x \), we set \( 10y-19 = 3y - 5 \).

Step2: Solve for \( y \)

Subtract \( 3y \) from both sides: \( 7y-19=-5 \). Then add 19 to both sides: \( 7y = 14 \), divide by 7: \( y = 2 \).

Step3: Find \( x \)

Substitute \( y = 2 \) into \( x = 3y - 5 \), so \( x=3\times2 - 5=6 - 5 = 1 \).

Answer:

The couple - solution is \( (x = 2, y = 10) \) or \( (2,10) \)

Part (b)