Question

Solve the following system of linear equations using elimination. 4x+3y=15 4x-3y=9

Answer 1

Given the system of equations:

`\begin{cases}4x+3y=15 \\ 4x-3y=9\end{cases}`

we can solve this system by elimination by adding both equations at the same time. Then, we have the following:

`\begin{gathered} 4x+3y=15 \\ 4x-3y=9 \\ ---------- \\ 8x+0y=24 \\ \Rightarrow8x=24 \\ \Rightarrow x=(24)/(8)=3 \\ x=3 \end{gathered}`

we have that x = 3. Now we can use this value on the first equation to find the value of y:

`\begin{gathered} 4(3)+3y=15 \\ \Rightarrow12+3y=15 \\ \Rightarrow3y=15-12=3 \\ \Rightarrow y=(3)/(3)=1 \\ y=1 \end{gathered}`

therefore, the solution of the system is the point (3,1)