Question

If 2x + 5y = -1 and 3x -2y = 27, then what is the value of x?

Answer 1

x = 7

Explanation:

Given system of equations:

`\begin{cases}2x+5y=-1\\3x-2y=27\end{cases}`

Multiply the first equation by 2:

`\implies 2(2x+5y)=2(-1)`

`\implies 4x+10y=-2`

Multiply the second equation by 5:

`\implies 5(3x-2y)=5(27)`

`\implies 15x-10y=135`

Add the two equations to eliminate the term in y:

`\begin{array}{crcccl}& 4x & + & 10y & = & \:-2\\+ & (15x & - & 10y & = & 135)\\\cline{2-6} & 19x & & & = & 133\\\cline{2-6}\end{array}`

Solve the equation for x:

`\implies 19x=133`

`\implies (19x)/(19)=(133)/(19)`

`\implies x=7`

Answer 2

• x = 7

--------------------------

Given system

• 2x + 5y = - 1,
• 3x - 2y = 27.

Eliminate y and solve for x

Multiply the first equation by 2 and the second equation by 5

• 2(2x) + 2(5y) = 2(-1) ⇒ 4x + 10y = - 2
• 5(3x) - 5(2y) = 5(27) ⇒ 15x - 10y = 135

Add up the equations

• 4x + 15x = - 2 + 135
• 19x = 133
• x = 133/19
• x = 7