Question

use the aleks graphing calculator to solve the system of equations. 0.55x - y = -4.1 0.4y = 2.8x + 8 round to the nearest hundredth.

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation \(0.55x - y=-4.1\), we can rewrite it as \(y = 0.55x + 4.1\).
For the second equation \(0.4y=2.8x + 8\), divide both sides by \(0.4\): \(y=\frac{2.8x + 8}{0.4}=\frac{2.8}{0.4}x+\frac{8}{0.4}=7x + 20\).

Step2: Set the two equations equal to each other

Since both are equal to \(y\), we have \(0.55x+4.1 = 7x+20\).

Step3: Solve for \(x\)

Subtract \(0.55x\) from both sides: \(4.1=7x - 0.55x+20\).
Simplify the right - hand side: \(4.1 = 6.45x+20\).
Subtract \(20\) from both sides: \(4.1-20=6.45x\).
\(- 15.9 = 6.45x\).
Divide both sides by \(6.45\): \(x=\frac{-15.9}{6.45}\approx - 2.4651\).

Step4: Solve for \(y\)

Substitute \(x\approx - 2.4651\) into \(y = 0.55x + 4.1\) (we could also use \(y = 7x+20\)).
\(y=0.55\times(-2.4651)+4.1\).
\(y=-1.3558+4.1\).
\(y = 2.7442\).

Answer:

The solution to the system of equations is \(x\approx - 2.47\) and \(y\approx2.74\) (rounded to the nearest hundredth).