Question

Match the system of equations on the left with the appropriate solution on the right.

2x+4y=7 (8,2)

x=7-2y (-1,-1)

3x+6y=-9 (1,3)

x=-2y-3 Infinite number of solutions

4x-2y-3 No solution

x=3y=2

Answer 1

`x=7-2y`
`(1,3)`

`3x+6y=-9`
`(-1,-1)`

`4x-2y-3`
`\text{no solution}`

`2x+4y=7`
`\text{infinite number of solutions}`

`x=-2y-3`
`(1,-2)`

Explanation:

1:
`x=7-2y`

`\Rightarrow x+2y=7`

`\Rightarrow (1,3)\;\text{is a solution of the above equation}.`

2:
`3x+6y=-9`

`\Rightarrow 3(-1)+6(-1)=-3-6=-9`

`\Rightarrow (-1,-1)\; \text{is a solution of the equation 3x+6y=-9}.`

3:
`4x-2y-3`

`\Rightarrow \;\text{It is not an equation}\\ \text{So, 4x-2y-3 has no solution.}`

4:
`2x+4y=7`

`\Rightarrow 2x+4y=7\;\text{have an infinite number of solutions.}\\\text{Because for every x there exists a value of y which satisfies the equation.}`

5:
`x=-2y-3`

`\Rightarrow x+2y=-3`

`\Rightarrow 1-2(-2)=1-4=-3`

`\Rightarrow (1,-2)\; \text{is a solution of the equation x=-2y-3}.`