Question

Sam and Kevin both worked hard over the summer. Together they earned a total of $425. Kevin earned $ 25 more than Sam.
a) Write a system of equations for the situation. Use s for the amount Same earned and k for the amount Kevin earned.
b) Graph the equations in the system.
c) Use your graph to estimate how much each person earned.


Solve the system of equations by substitution.
6= -4x + Y
-5x - Y =21

Solve the system by the elimination method.
2x + y=20
6x - 5y=12

Please help I do not understand how to do this ..Thanks

Answer 1

QUESTION 1

a)

Let

$s$

represent the amount Same earned and

$k$

represent the amount Kevin earned.

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

This implies that,

$k+s= 425---eqn(1)$

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

This implies,

$k-s=25---eqn(2)$

For equation (1), when

$s=0$

$k=425$

We plot the point,

$(425,0)$

When

$k=0$

$s=425$

We plot the point,

$(0,425)$

Similarly for the second equation when

$s=0$

$k=25$

This gives the point,

$(25,0)$

When

$k=0$

$s=-25$

We plot

$(0,-25)$

and draw a straight line through them.

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

$(225,200)$

This implies that

$k=225\:and\:s=200$

Therefore Kevin earned $ 225

and Same earned $ 200

QUESTION 2

The given system is

$6=-4x + y---eqn(1)$

and

$-5x-y=21---eqn(2)$

From equation (2),

$y=-5x-21---eqn(3)$

Put equation (3) into equation (1).

This implies that,

$6=-4x-5x-21$

Group like terms,

$6+21=-4x-5x$

Simplify, to get,

$27=-9x$

$x=-3$

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

$y=-5(-3)-21$

$y=15-21$

$y=-6$

Therefore the solution is

$(-3,-6)$

QUESTION 3

We want to solve,

$2x+y=20---(1)$

and

$6x -5y=12---(2)$

We multiply equation (1) by 3 to get,

$6x+3y=60---(3)$

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

$8y=48$

This means

$y=6$

Put this value into equation (1) to get,

$2x+6=20$

$2x=20-6$

$2x=14$

$x=7$

The solution is

$(7,6)$

Answer 2

Answer:

Sam earns $200 and Kevin earns $225.

x , y= -3 , -6 by substitution

x , y= 7, 6 by elimination

Step-by-step explanation:

a) Let the amount earned by Sam = s and the amount earned by Kevin = k

We are given, that they both earn total $425 i.e. s + k = 425

Also, Kevin earns $25 more than Sam i.e. k = s + 25

Hence, the system of equations comes out to be:

s + k = 425

-s + k = 25

b) Take s = x and k = y. See the graph plotted below

c) As the intersection point from the graph comes out to be (s,k) = (200,225)

Therefore, Sam earns $200 and Kevin earns $225.

Now, we have the system

-4x + y = 6

-5x - y = 21

We need to use substitution method.

Take y= -5x - 21 from the 2nd equation and put it in the 1st.

We get, -4x - 5x - 21 = 6  i.e.  -9x = 27  i.e.  x= -3

Now, substitute this value of x in any of the equation to find y.

We get, -5*(-3) - y = 21  i.e.  y = 15 - 21  i.e.  y = -6

Now, we are given the system,

2x + y = 20

6x - 5y = 12

We need to use elimination method.

Multiply 5 by equation 1. We get,

10x + 5y = 100

6x - 5y = 12

Adding the above equations, we get, 16x = 112  i.e. x = 7

Put this value in any of the equation to find the value of y.

We get, y = 20 - 2x  i.e.  y = 20 - 2*7  i.e.  y = 20 - 14  i.e. y = 6