please help me solve this eq. (simultaneous equation)?

Question

x + y = 10
x² + y² = 148

thank u!!!

Answer 1

An equation in 2 unknowns requires to separate equations to find the solution.

In the first equation, x + y = 10, solve for x
and you get:
x = - y + 10.

Now,
substitute that into the second equation so that
x squared + y squared = 148
becomes
(-y +10) squared +y = 148

Simplify that expression and solve

100 - 20y + y squared + y squared = 148

2y squared -20y + 100 = 148

2y squared - 20y - 48 = 0

(y -12)(y + 4) = 0

Y = 12 and Y = -4

Now, if x + y = 10 and Y = 12, then x = -2 (checks below)

if x + y = 10 and Y = -4, then x = 14 (does not check see below)

Test the answers by plugging the solutions for x and y into both equations. Hmm-m, both sets of numbers work for " x + y = 10" Wonder if they work for "x squared + y squared = 148 ???.

144 + 4 = 148 (Checks)
and
196 + 16 = 212 (wrong, do not support this solution, it was supposed to equal 148)

So circle the answer that checks as your final answer.
x = -2 and y = 12

Have a good day,
Zah

Answer 2

12 and -2
12 + -2 = 10
12^2 + -2^2 = 148
144 + 4 + 148

Answer 3

12 and -2.

It works well.

Answer 4

x = 10-y

substitute 10-y for x in the second equation and solve for y.

You can also use a matrix equation, but that would be more complicated for this problem.

Answer 5

x=10-y
x^2=100-20y+y^2

Substitute

100-20y+y^2+y^2=148
2y^2-20y=48
y^2-10y-24=0

Use the quadratic equation to complete

y=12, y=-2

Solve for x and check