Question

HELP ASAP PLZZZZ

Solve the following system of equations by linear combination: 3d – e = 7 d + e = 5

There is no solution. The solution is (2, –1). There are an infinite number of solutions. The solution is (3, 2). 1 points

QUESTION 2 Solve, using linear combination. 4x + y = 5 3x + y = 3

(0, –3) (0, 5) (–3, 7) (2, –3)
QUESTION 3 Solve using linear combination. a – 2b = –2 2a + 2b = 14

Which ordered pair in the form (a, b) is the solution to the system of equations?

(4, 3) (3, 4) (1, 6) (5, 3) 1 points

QUESTION 4 Solve, using linear combination. 11x + 4y = 18 3x + 4y = 2

(2, 0) (4, –5) (2, 1) (2, –1) 1 points

QUESTION 5 Solve the following system of equations by linear combination:

2d + e = 8 d – e = 4 There is no solution. The solution is (5, –2). There are an infinite number of solutions. The solution is (4, 0).'

Answer 1

QUESTION 1

The given system of equations is


`3d - e = 7...eqn(1)`

`d + e = 5...eqn(2)`

To solve by linear combination, we add equation (1) to equation (2) to get,


`3d + d= 7 + 5`



`4d = 12`


We divide through by 4 to obtain,



`d = (12)/(4)`



`d = 3`


We put d=3 into equation (2) to get,




`3+ e = 5`



`e = 5 - 3`



`e = 2`



`\boxed {The \: solution \: is \: (3, 2)}`



QUESTION 2


The given system is

4x + y = 5 ...eqn(1)

3x + y = 3 ...eqn(2)


To solve by linear combination, we subtract equation (2) from equation (1) to eliminate y from the equation.

This will give us,


`4x - 3x = 5 - 3`



This implies that,


`x = 2`


Put x=3 into equation (1) to get,


`4(2) + y = 5`


`8+ y = 5`



`y = 5 - 8`




`y = - 3`

The solution is


`(2,-3)`



QUESTION 3

We want to solve the system;


a – 2b = –2 ....eqn(1)


2a + 2b = 14...eqn(2)

by linear combination.


We need to add equation (1) to equation (2) to eliminate b.


This implies that,


`2a + a = 14 + - 2`




Simplify,


`3a = 12`



Divide both sides by 3 to get,



`a = 4`
Put a=4 into equation (2) to obtain,




`2(4) + 2b = 14`



`8 + 2b = 14`

`2b = 14 - 8`



`2b = 6`



`b = 3`


The ordered pair in the form (a, b) is


`(4,3)`



QUESTION 4

The given system of equations is


11x + 4y = 18 ...eqn(1)

3x + 4y = 2 ...eqn(2)


We subtract equation (2) from equation (1) to get,



`11x - 3x = 18 - 2`



`8x = 16`



`x = 2`


Put x=2 into equation (2) to obtain,



`3(2) + 4y = 2`


This implies that,



`6 + 4y = 2`



`4y = 2 - 6`



`4y = - 4`



`y=-1`

The correct answer is (2,-1).




QUESTION 5

The given system is ;

2d + e = 8...eqn1

d – e = 4...eqn2


We add the two equations to eliminate e.


This implies that,


`2d + d = 8 + 4`



`3d = 12`



We divide both sides by 3 to get,



`d = 4`


We put d=4 into equation (2) to get,


`4 - e = 4`


`- e = 4 - 4`




`- e = 0`




`e = 0`


The solution is


`(4,0)`