High School

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------------------------------------------------ Solve the following system of equations:

1. 4x + 12.8y = 39.4
2. 7x - 2.3y = -4.9

Answer :

To solve the system of equations given:


  1. [tex]4x + 12.8y = 39.4[/tex]

  2. [tex]7x - 2.3y = -4.9[/tex]


We can use the method of substitution or elimination. Here, I'll demonstrate using the elimination method:

Step 1: Align the equations

The system of equations is:
[\begin{align*}


  1. & \quad 4x + 12.8y = 39.4 \

  2. & \quad 7x - 2.3y = -4.9
    \end{align*}]


Step 2: Eliminate one variable

Let's eliminate [tex]x[/tex] by making the coefficients of [tex]x[/tex] in both equations equal. Multiply equation (1) by 7 and equation (2) by 4:

[tex]\begin{align*}
1.' & \quad 28x + 89.6y = 275.8 \\
2.' & \quad 28x - 9.2y = -19.6
\end{align*}[/tex]

Step 3: Subtract the equations

Subtract equation (2') from equation (1') to eliminate [tex]x[/tex]:

[tex]89.6y + 9.2y = 275.8 + 19.6[/tex]

[tex]98.8y = 295.4[/tex]

Step 4: Solve for [tex]y[/tex]

Divide both sides by 98.8:

[tex]y = \frac{295.4}{98.8} \approx 2.99[/tex]

Step 5: Substitute [tex]y[/tex] back into one of the original equations

Substitute [tex]y = 2.99[/tex] into equation (1):

[tex]4x + 12.8(2.99) = 39.4[/tex]

[tex]4x + 38.272 = 39.4[/tex]

Subtract 38.272 from both sides:

[tex]4x = 1.128[/tex]

Divide by 4:

[tex]x = \frac{1.128}{4} \approx 0.282[/tex]

So, the solution to the system of equations is approximately [tex]x \approx 0.282[/tex] and [tex]y \approx 2.99[/tex].

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