The system 3x plus 2y equals 18 and x minus y equals 4 asks for 4x plus y. Without Desmos, adding the two equations gives 4x plus y equals 22 in one step; in Desmos, it takes typing both equations, clicking their intersection at (5.2, 1.2), and calculating 4 times 5.2 plus 1.2. Next, the equation x squared minus 3.4x minus 5.1 equals 0 asks for its positive solution to the nearest hundredth: by hand, the quadratic formula takes four decimal calculations; in Desmos, after typing the equation, a gray pointer clicks where the positive solution crosses the x-axis, giving x approximately 4.53. Finally, the graphs of y equals (x squared minus 36) divided by (x minus 6) and y equals 12 appear to meet at (6, 12). Answer whether six satisfies the original equation using the buttons after the picture.
3x+2y=18
x−y=4
What is the value of 4x+y?
Without Desmos
Add the two equations4x+y=22
In Desmos
13x+2y=18
2x−y=4
3Intersection: (5.2,1.2)
44(5.2)+1.2=22
You’ll leave with these skills
01Identify what the answer must tell you
02Find extreme values or roots from an equation’s structure
03Find the requested expression without solving for every variable
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