Question

X^2+y^2=49 , y=7-x solve it in substitution

Answer 1

The system of equations x^2 + y^2 = 49 and y = 7 - x can be solved by substitution, resulting in the solutions (0, 7) and (7, 0).

Step-by-step explanation:

To solve the system of equations x2 + y2 = 49 and y = 7 - x using substitution, we substitute the second equation into the first one.

1. First, we take the equation y = 7 - x and plug it into y in the first equation, becoming x2 + (7 - x)2 = 49.
2. Simplify and solve the resulting equation x2 + 49 - 14x + x2 = 49 to 2x2 - 14x = 0.
3. Factor out x, giving x(2x - 14) = 0. Our possible solutions for x are 0 or 7.
4. By substituting x back into y = 7 - x, we find our solutions for y, which are 7 and 0, respectively.
5. Therefore, the solutions to the system of equations are (0, 7) and (7, 0).

Answer 2

x^2+(7-x)^2=49
x^2+x^2-14x+49=49
2x^2-14x=0
2x(x-7)=0
x=0, x=7