Question

x-y =7
x² + y = 149
simultaneous equations
​

Answer 1

Answer:

If x-y=3 and x²+y²=185, what is x and y?

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Tipper Rumpf

Answered 2 years ago

Well, let’s see. We start with

x−y=3

x2+y2=185

The first equation is the equation of a line. The second equation is the equation for a circle centered at zero. If the line does not touch the circle, there will be no solutions. If the line just touches the circle as a tangent, there will be only one solution. Otherwise, the line will cross two parts of the circle and there will be two solutions.

Step 1 — Solve line equation for y

y=x−3

Step 2 — Substitute this into the circle equation.

x2+(x−3)2=185

Step 3 — Solve Step 2 equation for x

x2+x2−6x+9=185

2x2−6x−176=0

x2−3x−88=0

Step 4 — Apply quadratic equation to calculate x

x=−(−3)±(−3)2−4(1)(−88)√2(−88)

x1=11 and x2=−8

Step 5 — Plug these values into the equation in Step 1 to get y

y1=x1−3=11−3=8

y2=x2−3=−8−3=−11

The final answers are (11,8) and (-8,-11)