Solve by Element List Regression

System of Linear Equations (No Solution) on the SAT: Desmos Walkthrough

This lesson uses sliders and direct evaluation in Desmos: put the unknown constant on a slider or a single expression line and let the calculator find the value instead of solving algebra by hand.

A real SAT-style question

How to solve it in Desmos, step by step

1. 1

   Step 1

   Type the first equation exactly as written. Desmos draws it as a straight line, no need to solve for y.

   Type in Desmos

   $4x-9y=9y+5$
2. 2

   Step 2

   On the next line, type the second equation. Because it contains h, Desmos offers to add a slider for h, so click add slider.

   Type in Desmos

   $hy=2+4x$
3. 3

   Step 3

   Drag the h slider and watch the second line rotate. For most values it crosses the first line at one point, a single solution. Keep increasing h until the two lines become parallel and stop crossing, which happens at h equals 18.

   Type in Desmos

   $h=18$
4. 4

   Step 4

   At h equals 18 the lines are parallel with different intercepts, so they never meet and the system has no solution. The answer is 18, which is choice D.

Now you try one

Same question type, different numbers. Use the exact Desmos moves from the walkthrough above.

More Desmos SAT lessons