Question

What is the answer for the equation

Answer 1

2x+3y=7

3x+4y=10

by combination:

-3(2x+3y=7)

2(3x+4y=10)

-6x-9y=-21

6x+8y=20

-y=-1

y=1

calculate x :

3x+4y=10

3x+4=10

3x=10-4

x=2

check:

2x+3y=7

2*2 + 3**1 = 7

Explanation:

Answer 2

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

Explanation:

we are given the system of equations:

`\begin{cases}2x+3y=7\\3x+4y=10\end{cases}`

now, we can multiply the first equation by 3 and the second by 2:

`\begin{cases}6x+9y=21\\6x+8y=20\end{cases}`

then, subtracting the two equations leads us with
`y=1.`

now, substituting back to the first equation, we have

`2x+3(1)=7\implies 2x=7-3\implies 2x=4\implies x=2`

therefore, we have our solution as
`(x,y)=(2,1)`