Question 10(multiple choice worth 1 points) (8.01 mc) two lines, a and b, are represented by the equations given below: line a: y = x − 6 line b: y = 3x + 4 which of the following shows the solution to the system of equations and explains why? (−5, −11), because the point satisfies both equations (−5, −11), because the point does not lie on any axis (−3, −5), because the point satisfies one of the equations (−3, −5), because the point lies between the two axes

y = x − 6

y = 3x + 4

y is isolated in both equations, thus, you can set x - 6 and 3x + 4 equal to each other to solve for x.

x - 6 = 3x + 4

-2x - 6 = 4

-2x = 10

x = -5

Substitute -5 for x into either of the original equations to find y.

y = x - 6

y = -5 - 6

y = -11

Plug both x- and y-values into each original equation to check whether these values satisfy both equations.

y = x - 6 --> -11 = -5 - 6 --> -11 = -11 --> True

y = 3x + 4 --> -11 = 3(-5) + 4 --> -11 = -15 + 4 --> -11 = -11 --> True

(−5, −11), because the point satisfies both equations.

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.