Question

Math algebra. 50 points!!!!!!

Answer 1

Given equations,

→ 3x - y = 6

→ 6x + y = 21

Forming the equation for y,

→ 6x + y = 21

→ y = -6x + 21

Now the value of x will be,

→ 3x - y = 6

→ 3x + 6x - 21 = 6

→ 9x = 6 + 21

→ x = 27/9

→ [ x = 3 ]

Then the value of y will be,

→ y = -6x + 21

→ y = -6(3) + 21

→ y = -18 + 21

→ [ y = 3 ]

Now the value of x and y is,

→ x = 3, y = 3

Hence, the value of both is 3.

Answer 2

x = 3, y = 3

Explanation:

Given system of equations:

`\begin{cases}3x-y=6\\6x+y=21 \end{cases}`

Add the two equations to eliminate y:

`\begin{array}{crcccl}& 3x & - & y & = & \phantom{.}6\\+ & (6x & + & y & = & 21)\\\cline{2-6}& 9x &&&=&27\\\cline{2-6}\end{aligned}`

Solve for x:

`\implies 9x=27`

`\implies x=\frac{27}9}`

`\implies x=3`

Substitute the found value of x into one of the equations and solve for y:

`\implies 6x+y=21`

`\implies 6(3)+y=21`

`\implies 18+y=21`

`\implies y=21-18`

`\implies y=3`

Therefore, the solution to the given system of equations is:

• x = 3
• y = 3