Question

A+b=60 a-b=40 whats a/b?

Answer 1

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

$\boxed{ \ \left \{ {{px + qy = r} \atop {mx + ny = s}} \right \ }$

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

Given:

• $\boxed{ \ a + b = 60 \ }$ . . . (Equation-1)
• $\boxed{ \ a - b = 40 \ }$ . . . (Equation-2)

Question:

$\boxed{ \ \frac{a}{b} = ? \ }$

Problem solving

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

$\boxed{ \ a = b + 40 \ }$

Substituting this expression for a into the Equation-1 yields

$\boxed{ \ (b + 40) + b = 60 \ }$

$\boxed{ \ b + 40 + b = 60 \ }$

$\boxed{ \ 2b = 60 - 40 \ }$

$\boxed{ \ 2b = 20 \ }$

$\boxed{\boxed{ \ b = 10 \ }}$

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

$\boxed{ \ a = 10 + 40 \ }$

$\boxed{\boxed{ \ a = 50 \ }}$

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

_______ +

$\boxed{ \ 2a = 100 \rightarrow \boxed{ \ a = 50 \ } \ }$

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

a + b = 60

a - b = 40

_______ -

$\boxed{ \ 2b = 20 \rightarrow \boxed{ \ b = 10 \ } \ }$

Note:

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

$\boxed{ \ 50 + 10 = 60 \ }$ . . . (Equation-1) $\boxed{ \checkmark }$

$\boxed{ \ 50 - 10 = 40 \ }$ . . . (Equation-2) $\boxed{ \checkmark }$

Now we calculate the value of a/b.

$\boxed{ \ \frac{a}{b} = \frac{50}{10} \ }$

Thus, $\boxed{\boxed{ \ \frac{a}{b} = 5 \ }}$

Learn more

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3. The midpoint 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

Answer 2

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