Question

e -0.8x + 8,6y = -7,2 et 1,4x - 4,3y = 9,3
(-0,8x + 8,6y = -7,2)
0,8·(1,4x - 4,3y = 9,3)
... (handwritten calculations)
réponse y = -1,129

Explanation:

Step1: Multiply the second equation

To eliminate \( y \), multiply the second equation \( 1.4x - 4.3y = 9.3 \) by \( 2 \) (since \( 8.6 = 2\times4.3 \)).
New second equation: \( 2\times(1.4x - 4.3y)=2\times9.3 \)
Simplify: \( 2.8x - 8.6y = 18.6 \)

Step2: Add the two equations

Now we have the first equation \( -0.8x + 8.6y = -7.2 \) and the new second equation \( 2.8x - 8.6y = 18.6 \).
Add them: \( (-0.8x + 8.6y)+(2.8x - 8.6y)= -7.2 + 18.6 \)
Simplify: \( (-0.8x + 2.8x)+(8.6y - 8.6y)= 11.4 \)
Which gives: \( 2x = 11.4 \)

Step3: Solve for \( x \)

Divide both sides by \( 2 \): \( x=\frac{11.4}{2}=5.7 \)

Step4: Substitute \( x \) into an equation

Substitute \( x = 5.7 \) into the first equation \( -0.8x + 8.6y = -7.2 \):
\( -0.8\times5.7 + 8.6y = -7.2 \)
Calculate \( -0.8\times5.7=-4.56 \):
\( -4.56 + 8.6y = -7.2 \)
Add \( 4.56 \) to both sides: \( 8.6y = -7.2 + 4.56=-2.64 \)
Solve for \( y \): \( y=\frac{-2.64}{8.6}\approx - 0.307 \) (Wait, the handwritten solution has an error. Let's recalculate correctly.)

Wait, let's redo Step4 with correct arithmetic:
From \( -0.8x + 8.6y = -7.2 \), \( x = 5.7 \):
\( -0.8(5.7)=-4.56 \)
So \( -4.56 + 8.6y = -7.2 \)
Add \( 4.56 \): \( 8.6y = -7.2 + 4.56=-2.64 \)
\( y=\frac{-2.64}{8.6}=\frac{-264}{860}=\frac{-66}{215}\approx - 0.307 \). But the handwritten solution has a mistake. Let's check the original handwritten steps. The handwritten multiplication seems incorrect (0.8 instead of 2). Correcting the method:

Alternative (correct) method:
Original equations:

1. \( -0.8x + 8.6y = -7.2 \)
2. \( 1.4x - 4.3y = 9.3 \)

Multiply equation 2 by 2: \( 2.8x - 8.6y = 18.6 \) (correct step).
Add to equation 1: \( (-0.8x + 2.8x)+(8.6y - 8.6y)= -7.2 + 18.6 \)
\( 2x = 11.4 \Rightarrow x = 5.7 \) (correct).

Substitute \( x = 5.7 \) into equation 2: \( 1.4(5.7)-4.3y = 9.3 \)
\( 7.98 - 4.3y = 9.3 \)
\( -4.3y = 9.3 - 7.98 = 1.32 \)
\( y=\frac{1.32}{-4.3}\approx - 0.307 \) (Wait, sign error! \( 9.3 - 7.98 = 1.32 \), so \( -4.3y = 1.32 \Rightarrow y = -\frac{1.32}{4.3}\approx - 0.307 \). The handwritten solution has an error in calculation, but following correct steps:

Wait, maybe the original handwritten had a typo in coefficients. Let's assume the equations are correct as given: \( -0.8x + 8.6y = -7.2 \) and \( 1.4x - 4.3y = 9.3 \). The correct solution for \( x = 5.7 \), \( y\approx - 0.31 \) (rounded). But the handwritten solution has a mistake in intermediate steps. However, following the elimination method:

Answer:

The correct solution is \( x = 5.7 \), \( y\approx - 0.31 \) (Note: The handwritten solution has calculation errors; the above is the correct method.)