Question 94·Easy·Nonlinear Equations in One Variable; Systems in Two Variables
Which ordered pair satisfies the system of equations?
For systems where one equation is very simple (like or ), first solve that equation to fix one variable. Then substitute that value into the other (often nonlinear) equation to find the second variable. Finally, match your pair to the choices, and as a quick check, plug the pair back into both equations to confirm it satisfies the system.
Hints
Use the simpler equation first
Look at the equation . What single value of makes this true?
Substitute into the second equation
Once you know , plug that value into . Be careful with parentheses and the exponent.
Check against all choices
After you find and , write them as an ordered pair and see which answer choice has the same pair.
Desmos Guide
Graph the first equation
In Desmos, type x - 4 = 0. Desmos will show a vertical line where this equation is true.
Graph the second equation
On a new line, type y = (x - 4)^2 + 1. This will draw a parabola opening upward.
Find the intersection point
Look for the point where the vertical line and the parabola intersect. Tap that intersection point and read off its coordinates; that ordered pair is the solution to the system and should match one of the answer choices.
Step-by-step Explanation
Solve the first equation for x
From the first equation:
Add 4 to both sides:
So any solution to the system must have .
Substitute x into the second equation
Now use in the second equation:
Substitute :
Simplify inside the parentheses first:
So we have:
Then square and add:
Form the ordered pair and match to the choices
We found and , so the solution to the system is the ordered pair .
Among the answer choices, this matches choice D.