Question

use the aleks graphing calculator to solve the system of equations.
$5 - 0.7x = 0.2y$
$-y + 0.4x = 1.8$
round to the nearest hundredth.
$(x, y) = (\square, \square)$

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation \(5 - 0.7x=0.2y\), we can rewrite it as \(y=\frac{5 - 0.7x}{0.2}=\frac{5}{0.2}-\frac{0.7x}{0.2}=25 - 3.5x\).
For the second equation \(-y + 0.4x=1.8\), we can rewrite it as \(y = 0.4x-1.8\).

Step2: Set the two equations equal to each other

Since both are equal to \(y\), we set \(25-3.5x=0.4x - 1.8\).

Step3: Solve for \(x\)

Add \(3.5x\) to both sides: \(25=0.4x+3.5x - 1.8\)
Simplify: \(25 = 3.9x-1.8\)
Add \(1.8\) to both sides: \(25 + 1.8=3.9x\)
\(26.8 = 3.9x\)
Divide both sides by \(3.9\): \(x=\frac{26.8}{3.9}\approx6.87\)

Step4: Solve for \(y\)

Substitute \(x\approx6.87\) into \(y = 0.4x-1.8\)
\(y=0.4\times6.87-1.8=2.748 - 1.8 = 0.948\approx0.95\)

Answer:

\((x,y)\approx(6.87,0.95)\)