Question

X/a+y/b=2
ax-by=a2-b2 solve by substitution method

Answer 1

Answer:

Step-by-step explanation:

xa+yb=2

ax−by=a2−b2

Rewrite the first equation in a more beautiful form. Multiply it throughout by ab.

bx+ay=2ab

The coefficients of the variables are interchanged between the two equations. I assume that by cross multiplication, you mean making the coefficients equal, so that a simple subtraction of the equations will eliminate a variable.

Multiply the first equation by a and the second by b.

abx+a2y=2a2b

abx−b2y=a2b−b3

Subtract them.

(a2+b2)y=(a2+b2)b

⟹y=b

Substituting this value in any of the above equations will yield the value of x.

bx+ay=2ab

⟹bx+ab=2ab

⟹x=a

Answer 2

Step-by-step explanation:

Given:

$\frac{x}{a} + \frac{y}{b} = 2...eq1 \\ \\ ax - by = {a}^{2} - {b}^{2}...eq2$

To find: Solve given linear equations

Solution:

Step 1: Take LCM and simplify eq1

$\frac{x}{a} + \frac{y}{b} = 2 \\ \\ \frac{bx +ay}{ab} = 2 \\ \\ or \\ \\ bx +ay = 2ab...eq3$

Step 2: Take value of x from eq3 and put in eq2

$a. \frac{(2ab - ay)}{b} - by = {a}^{2} - {b}^{2} \\ \\ \frac{2 {a}^{2} b - {a}^{2}y - {b}^{2} y }{b} = {a}^{2} - {b}^{2} \\ \\ - y({a}^{2} + {b}^{2} ) = {a}^{2} b - {b}^{3} - 2 {a}^{2} b \\ \\ - y({a}^{2} + {b}^{2} ) = - {a}^{2} b - {b}^{3} \\ \\ y({a}^{2} + {b}^{2} ) = b({a}^{2} + {b}^{2}) \\ \\ y = \frac{b \cancel{({a}^{2} + {b}^{2})}}{ \cancel{({a}^{2} + {b}^{2})}} \\\\y=b$

Step 3: Put the value of y in eq2

$ax -b^{2} = {a}^{2} - {b}^{2} \\ \\ ax = {a}^{2} - {b}^{2} +b^{2} \\ \\ ax = a^2 \\ \\ x = \frac{ {a}^{2}}{a} \\ \\ x = a$

Final answer:

Values of x and y are

$\boxed{x = a} \\ \\\boxed{ y = b}$

Hope it helps you.

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