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# Find the sum of the x values which solve the system of equations

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Find the sum of the x values which solve the system of equations $$3y - 49 = 0 \\ x^2 + y^2 - 281 = 0$$

Nov 14, 2017

#1
+1965
+3

3y - 49 = 0

x^2 + y^2 - 281 = 0

First I would isolate the variable (y) in the first equation

3y - 49 = 0

3y = 49

Divide by 3 on both sides

y = 49/3

Then take your new equation and plug it into the second equation

x^2 + (49/3)^2 - 281 = 0

Simplify

x^2 + (2401/9) - 281 = 0

Subtract 281 from the fraction

x^2 + (-128/9) = 0

x^2 = (128/9)

Root on both sides

|x| = $$\sqrt{\frac{128}{9}}$$

Simplify (the x is a multiplication)

|x| = $$\frac{\sqrt{64 x 2}}{3}$$

Simplify again

|x| = $$\frac{8\sqrt{2}}{3}$$

Then the absolute value turns the other side into ±

x = ±$$\frac{8\sqrt{2}}{3}$$

Nov 14, 2017
edited by saseflower  Nov 14, 2017

#1
+1965
+3

3y - 49 = 0

x^2 + y^2 - 281 = 0

First I would isolate the variable (y) in the first equation

3y - 49 = 0

3y = 49

Divide by 3 on both sides

y = 49/3

Then take your new equation and plug it into the second equation

x^2 + (49/3)^2 - 281 = 0

Simplify

x^2 + (2401/9) - 281 = 0

Subtract 281 from the fraction

x^2 + (-128/9) = 0

x^2 = (128/9)

Root on both sides

|x| = $$\sqrt{\frac{128}{9}}$$

Simplify (the x is a multiplication)

|x| = $$\frac{\sqrt{64 x 2}}{3}$$

Simplify again

|x| = $$\frac{8\sqrt{2}}{3}$$

Then the absolute value turns the other side into ±

x = ±$$\frac{8\sqrt{2}}{3}$$

saseflower Nov 14, 2017
edited by saseflower  Nov 14, 2017
#2
0

x = +or-​ 8sqrt(2)/3

Nov 14, 2017
#3
+1965
+3

Thank you so much! I fixed it

saseflower  Nov 14, 2017
#4
+98197
+2

And..as saseflower would say....the sum of the x values that solve this system is just  0

Nov 14, 2017