Hello: ) anyone able to with this question ? you!

oh ignore my workings haha : )

( in the pic above )

look at the photo below for the Answer.

:)

Explanation:

Multiply both sides by the denominator a+b*sqrt(7). Then expand out the RHS and get that RHS into the form p+q*sqrt(7), where p and q are algebraic expressions.

2+4*sqrt(7) = (4-sqrt(7))(a+b*sqrt(7))

2+4*sqrt(7) = 4(a+b*sqrt(7))-sqrt(7)*(a+b*sqrt(7))

2+4*sqrt(7) = 4a+4b*sqrt(7)-a*sqrt(7)-7b

2+4*sqrt(7) = (4a-7b)+(4b-a)*sqrt(7)

The (4a-7b) part on the RHS matches up with 2 on the LHS, so

2 = 4a-7b or 4a-7b = 2

Similarly, the (4b-a)*sqrt(7) on the RHS matches up with 4*sqrt(7)

So,

4*sqrt(7) = (4b-a)*sqrt(7)

4 = 4b-a

-a+4b = 4

We have this system of equations

4a-7b = 2 and -a+4b = 4

Let's solve the second equation for a

-a+4b = 4

4b = 4+a

4b-4 = a

a = 4b-4

Plug this into the first equation; solve for b.

4a - 7b = 2

4( a ) - 7b = 2

4(4b-4)-7b = 2

16b-16-7b = 2

9b-16 = 2

9b = 18

b = 2

From here, we can compute the value of 'a'

a = 4b-4

a = 4(2)-4

a = 4

Your method of rationalizing the denominator would work out, though it seems like it would involve more steps.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1