Respuesta :

A is equal to 50 since 50+10=60 and 50-10=40 so that means b=10. a/b would be 50/10 which is equal to 5
BladeRunner212

a/b = 5

Further explanation

We begin by considering a system of linear equations in two variables. Recall that such a system may be written in the general form

[tex]\boxed{ \ \left \{ {{px + qy = r} \atop {mx + ny = s}} \right \ }[/tex]

where p, q, m, n, r, and s are real constants and neither p and q nor m and n are both zero.

Given:

  • [tex]\boxed{ \ a + b = 60 \ }[/tex] . . . (Equation-1)
  • [tex]\boxed{ \ a - b = 40 \ }[/tex] . . . (Equation-2)

Question:

[tex]\boxed{ \ \frac{a}{b} = ? \ }[/tex]

Problem solving

Solving the Equation-2 for a in terms of b, we obtain the equation

[tex]\boxed{ \ a = b + 40 \ }[/tex]

Substituting this expression for a into the Equation-1 yields

[tex]\boxed{ \ (b + 40) + b = 60 \ }[/tex]

[tex]\boxed{ \ b + 40 + b = 60 \ }[/tex]

[tex]\boxed{ \ 2b = 60 - 40 \ }[/tex]

[tex]\boxed{ \ 2b = 20 \ }[/tex]

[tex]\boxed{\boxed{ \ b = 10 \ }}[/tex]

Finally, substituting this value of b into the expression of a obtained earlier gives

[tex]\boxed{ \ a = 10 + 40 \ }[/tex]

[tex]\boxed{\boxed{ \ a = 50 \ }}[/tex]

Therefore, the unique solution of the system is given by a = 50 and b = 10.

Another way is to use elimination.

We eliminate variable b by adding both of the equations.

a + b = 60

a - b = 40

_______ +

[tex]\boxed{ \ 2a = 100 \rightarrow \boxed{ \ a = 50 \ } \ }[/tex]

And we eliminate variable a by subtracting both of the equations.

a + b = 60

a - b = 40

_______ -

[tex]\boxed{ \ 2b = 20 \rightarrow \boxed{ \ b = 10 \ } \ }[/tex]

Note:

We can check our result by substituting the values of a = 50 and b = 10 into the equations. Thus,

[tex]\boxed{ \ 50 + 10 = 60 \ }[/tex] . . . (Equation-1) [tex]\boxed{ \checkmark }[/tex]

[tex]\boxed{ \ 50 - 10 = 40 \ }[/tex] . . . (Equation-2) [tex]\boxed{ \checkmark }[/tex]

Now we calculate the value of a/b.

[tex]\boxed{ \ \frac{a}{b} = \frac{50}{10} \ }[/tex]

Thus, [tex]\boxed{\boxed{ \ \frac{a}{b} = 5 \ }}[/tex]

Learn more

  1. A linear programming problem https://brainly.com/question/3799248
  2. Determine the equation represents Nolan’s line  https://brainly.com/question/2657284  
  3. The midpoint https://brainly.com/question/3269852

Keywords: a + b = 60, a - b = 40, what is a/b?,  a system of linear equations in two variables., real constants, the general form, expression, the unique solution