Solve this system of equations without graphing:
[tex]\begin{gathered} 5x+2y=29\ldots\ldots(1) \\ 5x-2y=41\ldots\ldots(11) \end{gathered}[/tex]
Using Elimination Method:
[tex]\begin{gathered} 5x+2y=29\text{ } \\ \frac{-5x-2y=41}{4y=-12} \\ \text{divide both side by 4} \\ \frac{4y}{4}=\frac{-12}{4} \\ y=-3 \end{gathered}[/tex]
Substitute the value of y in equation (1):
[tex]\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} \\ \frac{5x}{5}=\frac{35}{5} \\ x=7 \end{gathered}[/tex]
Therefore the value of the x = 7 and y = -3
Hence the correct answer for the system of equation is (x, y) = (7 , -3)
