Question

Solve the System of Equations using Elimination. 3x - y =9 5x + y = 7

Answer 1

The solution to the System of equations is;

`\begin{gathered} x=2 \\ y=-3 \end{gathered}`

Step-by-step explanation:

Given the System of Equations;

`\begin{gathered} 3x-y=9 \\ 5x+y=7 \end{gathered}`

Solving by elimination.

to eliminate y, let add equation 1 and 2 together;

`\begin{gathered} 3x-y+5x+y=9+7 \\ 3x+5x-y+y=16 \\ 8x=16 \\ \text{divide both sides by 8;} \\ (8x)/(8)=(16)/(8) \\ x=2 \end{gathered}`

Since we have the value of x let us now substitute into equation 2 to get the value of y;

`\begin{gathered} 5x+y=7 \\ 5(2)+y=7 \\ 10+y=7 \\ y=7-10 \\ y=-3 \end{gathered}`

Therefore, the solution to the System of equations is;

`\begin{gathered} x=2 \\ y=-3 \end{gathered}`