Question

Solve this system of equations without graphing: 5x + 2y = 29 5x - 2y =41

Answer 1

Solve this system of equations without graphing:

`\begin{gathered} 5x+2y=29\ldots\ldots(1) \\ 5x-2y=41\ldots\ldots(11) \end{gathered}`

Using Elimination Method:

`\begin{gathered} 5x+2y=29\text{ } \\ (-5x-2y=41)/(4y=-12) \\ \text{divide both side by 4} \\ (4y)/(4)=(-12)/(4) \\ y=-3 \end{gathered}`

Substitute the value of y in equation (1):

`\begin{gathered} 5x+2y=29 \\ 5x+2(-3)=29 \\ 5x-6=29 \\ \text{Add 6 from both side} \\ 5x-6+6=29+6 \\ 5x=35 \\ \text{divide both side by 5} \\ (5x)/(5)=(35)/(5) \\ x=7 \end{gathered}`

Therefore the value of the x = 7 and y = -3

Hence the correct answer for the system of equation is (x, y) = (7 , -3)