The sum of the digits of a certain two-digit numnber is 13. The difference is -1. What is the two digit number?

Question

i need help with this it is on solving systems

Answer 1

Let x=first digit

y=second digit

You have 2 unknowns, so you must have 2 equations to solve this.

Eq. 1: x+y=13

Eq. 2: x-y=-1

You can use either the substitution of elimination method to solve this. Let's use the substitution method.

Using Eq. 2 we can solve for x in terms of y:

x-y=-1 Eq. 2

x-y+y=-1+y add y to both sides to isolate x

x=y-1 x is now in terms of y

Using this value of x we can "substitute" this x value into Eq. 1 and solve for y:

x+y=13 Eq. 1

y-1+y=13 substituting y-1 for x

2y-1+1=13+1 adding 1 to both sides to isolate the y term

2y=14 result

2y/2=14/2 divide both sides by 2

y=7 answer for y

Now put this value of y in either equation and solve for x:

x+y=13 Eq. 1

x+7=13 substitute value found for y, 7

x+7-7=13-7 subtract 7 from both sides of the equation to isolate x

x=6

Therefore, your 2 digits are x=6 and y=7 and the number is xy, or 67.

Hope this helps!

Answer 2

Let the two digits be a and b

a + b = 13 {Since, sum of the two digits is 13}

a - b = -1 {Since, difference is -1}

Solving both the equations, we get

a + b = 13

a - b = -1

----------------

2a = 12

a = 6

b = 13-6

b = 7

So, the number is 67

Answer 3

Let x = one digit of the number

Let y = the other digit of the number

The 2 equations are:

x+y=13

x-y=-1

To solve by elimination, add the equations together

2x=12 Divide both sides by 2

x=6

Plugging into the first equation to solve for y

6+y=13 Subtract 6 from both sides

y=7

The 2 digit number is 67

Answer 4

Let x and y be the digits:

The sum of the digits is 13

x + y = 13

The difference of the digits is -1

x - y = -1

Add those two equations togther:

2x = 12

Solve for x, the first digit

x = 6

Plug in value of 6 to solve for y, the second digit

6- y = -1

-y = -7

y = 7

The number is 67

Answer 5

Let's name each of the digits of the 2-digit number for a sec. How about the first digit is "a", and the second is "b".

If the sum of the digits is 13, then a+b = 13.

If the difference is -1, then a-b= -1.

We therefore have the system...

a+b=13

a-b= -1 , this is perfect for elimination!

Let's add the columns of a, b, and the constants. The resulting equation then is 2a= 12, so a=6.

You can then plug "a" back in to either original equation in order to find "b" (top or bottom). I'll use the top.

6+b=13

b=7.

Therefore the number is 67. We can check it, as 6+7=13 and 6-7=-1. Hooray!