Question

Solve the equations x squared + y squared = 36 x = 2y + 6

Answer 1

Answer:

Given the equations:

$x^2+y^2 =36$              .....[1]

$x =2y +6$                     ....[2]

Substitute the value of x in [1] we get;'

$(2y+6)^2+y^2 =36$

Use identity: $(a+b)^2= a^2+2ab+b^2$

$4y^2+36+24y + y^2 =36$

Combine like terms;

$5y^2+36+24y=36$

Subtract 36 from both sides we get;

$5y^2+24y=0$

$y (5y+24) = 0$

By zero product property, we get;

y = 0 and $y =- \frac{24}{5} = -4.8$

Substitute these y values in [2] to get x values;

For y = 0 we have;

x = 2(0) +6 = 0+6 = 6

For x = -4.8

x = 2(-4.8)+6 = -9.6 + 6 = -3.6

Therefore, the solution for the given equations are; (6, 0) and (-3.6, -4.8)