Solutions for systems of equations 1. which of the following statements would be the process that is used to describe solving a system of equation with 6 variables? solving a 3 order system solving a 6 order system solving a system solving an order system 2. determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. 2x - y = 7 2y = 4x - 14 {} 1 solution infinite 3. determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. x + y = 5 x + y = 7 {} 1 solution infinite 4. which of the following points is a solution to the system of equations shown? y - x = -1 x + y = -5 (-3, -2) (-6, 1) (-2, -3) 5. determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. x + y = 4 x - y = 0 {} 1 solution infinite 6. determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. 3x + 2y = 6 x - y = 2 {} 1 solution infinite 7.which of the following points is a solution to the system of equations shown? 4x + y = 1 y = x + 6 (5, -1) (0, 6) (-1, 5) 8.determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. x - y = 5 2x + y = 1 {} 1 solution infinite

1. Solving an order system

2. Let us solve this one by combining the two equations:

2x – y = 7

2y = 4x – 14 --> y = 2x – 7

combine:

2x – (2x – 12) = 7

2x – 2x + 7 = 7

0 + 7 = 7

7 = 7

No variable at the end, therefore infinite solutions

3. From the given equations itself, we can see that this is impossible to have solutions, therefore:

{}

4. y – x = -1 --> y = x – 1

x + (x – 1) = -5

2x – 1 = -5

x = -2

y = x – 1 = -2 – 1 = -3

(-2, -3)

5. x = y

x + x = 4

2x = 4

x = 2 = y

(2, 2)

1 solution

6. x – y = 2 --> x = 2 + y

3 (2 + y) + 2y = 6

6 + 3y + 2y = 6

5y = 0

y = 0

x = 2 + y = 2

(0, 2)

1 solution

7. 4x + (x + 6) = 1

5x + 6 = 1

5x = -5

x = -1

y = x + 6 = -1 + 6 = 5

(-1, 5)

8. x – y = 5 --> x = 5 + y

2 (5 + y) + y = 1

10 + 2y + y = 1

3y = -9

y = -3

x = 5 + y = 5 – 3 = 2

(2, -3)

1 solution

4 candies

step-by-step explanation:

7 x 28 = 196

200 - 196 = 4 candies remaining.

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.