2x + y =20
6x - 5y = 12
Solve as a whole number

QUESTION 1

a)

Let

represent the amount Same earned and

represent the amount Kevin earned.

We were told that, they earned $425 dollars together.

This implies that,

It was also given that, Kevin earned $25 more than Same.

This implies,

For equation (1), when

We plot the point,

When

We plot the point,

Similarly for the second equation when

This gives the point,

When

We plot

and draw a straight line through them.

We can see from the graph that the two points intersect at  

This implies that

Therefore Kevin earned $ 225

and Same earned $ 200

QUESTION 2

The given system is

and

From equation (2),

Put equation (3) into equation (1).

This implies that,

Group like terms,

Simplify, to get,

We substitute this value into equation (3) to get,

Therefore the solution is

QUESTION 3

We want to solve,

and

We multiply equation (1) by 3 to get,

Equation (3) minus equation (2) will give us,

This means

Put this value into equation (1) to get,

The solution is

QUESTION 1

a)

Let

represent the amount Same earned and

represent the amount Kevin earned.

We were told that, they earned $425 dollars together.

This implies that,

It was also given that, Kevin earned $25 more than Same.

This implies,

For equation (1), when

We plot the point,

When

We plot the point,

Similarly for the second equation when

This gives the point,

When

We plot

and draw a straight line through them.

We can see from the graph that the two points intersect at  

This implies that

Therefore Kevin earned $ 225

and Same earned $ 200

QUESTION 2

The given system is

and

From equation (2),

Put equation (3) into equation (1).

This implies that,

Group like terms,

Simplify, to get,

We substitute this value into equation (3) to get,

Therefore the solution is

QUESTION 3

We want to solve,

and

We multiply equation (1) by 3 to get,

Equation (3) minus equation (2) will give us,

This means

Put this value into equation (1) to get,

The solution is

2x + y = 20

6x - 5y = 20

2x + y = 20

Subtract 2x on both sides to get "y" by itself, so you can later substitute it into the second equation.

2x + y - 2x = 20 - 2x

y = 20 - 2x

6x - 5y = 12

6x - 5(20 - 2x) = 12   Multiply 5 into (20 - 2x)

6x - 100 + 10x = 12    Combine like terms

16x - 100 = 12     Add 100 on both sides  

16x - 100 + 100 = 12 + 100

16x = 112    Divide 16 on both sides to get "x" by itself

x = 7

Plug in x into either of the original equations to find y.

2x + y = 20

2(7) + y = 20

14 + y = 20

y = 6

x = 7, y = 6

x = 7, y = 6

(7,6)

Step-by-step explanation:

2x + y =20

6x - 5y = 12

2x + y = 20

-2x     -2x

y = -2x + 20

6x - 5y = 12

6x - 5(-2x + 20) = 12

6x + 10x - 100 = 12

16x - 100 = 12

     + 100  +100

16x = 112

/16    /16

x = 7

Now, we solve for y:

2x + y = 20

2(7) + y = 20

14 + y = 20

-14      -14

y = 6

(x, y) -> (7,6)

Hope this helps!

its (7,6)

Step-by-step explanation:

2x + y = 20

2(7) + 6 = 20

14 + 6 = 20

20 = 20

6x - 5y = 12

6(7) - 5(6) = 12

42 - 30 = 12

12 = 12

For 1st equation: 2(7)+6 = 14+6 = 20 = R.H.S

For 2nd equation: 6(7)-5(6)= 42-30 = 12 = R.H.S.

So, your answer is "YES" for both system of equations.

its (7,6)

Step-by-step explanation:

2x + y = 20

2(7) + 6 = 20

14 + 6 = 20

20 = 20

6x - 5y = 12

6(7) - 5(6) = 12

42 - 30 = 12

12 = 12

For 1st equation: 2(7)+6 = 14+6 = 20 = R.H.S

For 2nd equation: 6(7)-5(6)= 42-30 = 12 = R.H.S.

So, your answer is "YES" for both system of equations.

2x + y = 20

6x - 5y = 20

2x + y = 20

Subtract 2x on both sides to get "y" by itself, so you can later substitute it into the second equation.

2x + y - 2x = 20 - 2x

y = 20 - 2x

6x - 5y = 12

6x - 5(20 - 2x) = 12   Multiply 5 into (20 - 2x)

6x - 100 + 10x = 12    Combine like terms

16x - 100 = 12     Add 100 on both sides  

16x - 100 + 100 = 12 + 100

16x = 112    Divide 16 on both sides to get "x" by itself

x = 7

Plug in x into either of the original equations to find y.

2x + y = 20

2(7) + y = 20

14 + y = 20

y = 6

x = 7, y = 6