Answer :
To solve the system of equations given:
- [tex]4x + 12.8y = 39.4[/tex]
- [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*}
- & \quad 4x + 12.8y = 39.4 \
- & \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].
