Question

Please help, I really need it....

4. Which ordered pair is a solution to the system of equations? Use any method to solve.
2x - y = 5
3x + 2y = 4

A. (5,5)
B. (0,2)
C. (2,-1)
D. (-1,-7)


12. What is the solution to the system of equations? Use the linear combination method.

3x+2y=7
5x-4y=19

A. There are an infinite number of solutions.
B. The solution is (3,-1).
C. There is no solution.
D. The solution is (5, 1).

Answer 1

no 4.

using substitution method

2x - y = 5...(i)

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

making y subject of formula in (i)

2x-y=5

2x-5=y

substitute y in (ii)

3x+2(2x-5)=4

opening bracket

3x+4x-10=4

collecting like terms

3x+4x=4+10

7x=14

dividing both sides by 7

7x/7=14/7

x=2.

but y=2x-5

y=2(2)-5

y=-1.

solution=(2,-1)

no.12.

3x+2y=7...(i)

5x-4y=19...(ii)

multiply (i) by 2 and (ii) by 1

3x+2y=7}×2

5x-4y=19}×1

we get;

6x+4y=14

5x-4y=19

adding the two equations,

6x+5x=11x

4y+-4y=0

14+19=33

new equation

11x=33

divide both sides by 11

11x/11=33/11

x=3

replacing x in (i)

3x+2y=14

3(3)+2y=14

9+2y=14

2y=14-9

dividing both sides by 2

2y/2=5/2

y=5/2 or 2.5

solution=(3,5/2) which is not in the choices.