here ya go
Problem:
Solve the system of equations:
x2+y2=25x2+y2=25
x+y=7x+y=7
Step 1: Solve one of the equations for one variable.
From the second equation, we can express yy in terms of xx:
x+y=7x+y=7y=7−xy=7−x
Step 2: Substitute the expression for yy into the first equation.
Substitute y=7−xy=7−x into the first equation x2+y2=25x2+y2=25:
x2+(7−x)2=25x2+(7−x)2=25
Step 3: Expand the equation.
Expand the square term:
x2+(49−14x+x2)=25x2+(49−14x+x2)=25
Now simplify:
2x2−14x+49=252x2−14x+49=25
Step 4: Simplify and form a quadratic equation.
Move all terms to one side:
2x2−14x+49−25=02x2−14x+49−25=02x2−14x+24=02x2−14x+24=0

(x,y)=(4,3)(x,y)=(4,3

-rep

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