Question

1. résous le système linéaire suivant par élimination. vérifie la solution.

4x + 6y = 0
2x + 10y = 14

Explanation:

Step1: Label the equations

Let the first equation be \(4x + 6y = 0\) (Equation 1) and the second be \(2x + 10y = 14\) (Equation 2).

Step2: Eliminate x

Multiply Equation 2 by 2: \(2(2x + 10y)=2\times14\), which gives \(4x + 20y = 28\) (Equation 3).
Subtract Equation 1 from Equation 3: \((4x + 20y)-(4x + 6y)=28 - 0\).
Simplify: \(4x + 20y - 4x - 6y = 28\), so \(14y = 28\).

Step3: Solve for y

Divide both sides by 14: \(y=\frac{28}{14}=2\).

Step4: Substitute y into Equation 1

Substitute \(y = 2\) into \(4x + 6y = 0\): \(4x + 6\times2 = 0\), so \(4x + 12 = 0\).
Subtract 12: \(4x=-12\).
Divide by 4: \(x=\frac{-12}{4}=-3\).

Step5: Verify the solution

Check in Equation 1: \(4(-3)+6(2)=-12 + 12 = 0\) (correct).
Check in Equation 2: \(2(-3)+10(2)=-6 + 20 = 14\) (correct).

Answer:

The solution is \(x = - 3\) and \(y = 2\).