Question

Solve the pair of linear equations 2x-y =11 and 5 x+4y=1 by method of Substitution. Then find m which satisfies y=mx-11

Answer 1

Answer:

m =2

2x-y =11

5x-4y =1

5x+4(2x-1)=1

x= 45/13

y= -53/13

-53/13=m45/13 -11

m=2

Step-by-step explanation:

Answer 2

Given,

Pair of linear equations,

2x - y = 11,

5x + 4y = 1

To find,

Solution of above equations,

Value of m satisfying y = mx - 1.

Solution,

To solve a given pair of linear equations, first, we determine the value of a variable from one equation and then substitute this obtained expression in the other equation.

So, here, the given equations are,

2x - y = 11, and

5x + 4y = 1

We can see from first equation,

y = 2x - 11

Substituting this expression in the second equation, we get,

5x + 4(2x - 11) = 1

Simplifying the above equation,

5x + 8x - 44 = 1

⇒ 13x - 44 = 1

⇒ 13x = 45

⇒ $x=\frac{45}{13}$

Substituting this value of x in y = 2x - 11, we get,

$y=2(\frac{45}{13} )-11$

⇒ $y =\frac{-53}{13}$

Now, to find the value of m which satisfies y = mx - 11 for the given conditions, we can put the obtained values of x and y in this equation. So,

$\frac{-53}{13} =m(\frac{45}{13} )-11$

Rearranging,

$m(\frac{45}{13} )=11-\frac{53}{13}$

⇒ 45m = 143 - 53

⇒ $m = \frac{90}{45}$

⇒ m = 2.

Therefore, for given pair of equations, x = 45/13, y = -53/13, and m = 2.