Question

Section 1/3 (From our Algebra 2 textbook) Solve the system of linear equations in two variables by elimination or substitution. 33. 3x + y =7 - 2x - y =9

Answer 1

The solution to the given system of linear equation is;

`\begin{gathered} x=16 \\ y=-41 \end{gathered}`

Step-by-step explanation:

Given the linear system of equation;

`\begin{gathered} 3x+y=7\text{ ---------------1} \\ -2x-y=9​\text{ --------------2} \end{gathered}`

We want to solve the simultaneous equation by elimination.

We need to eliminate either x or y. from the given equation, we can see that by adding equation 1 and 2 together we can eiminate y;

So, let's add equation 1 and 2 together;

`\begin{gathered} 3x-2x+y-y=7+9 \\ x=16 \end{gathered}`

Since we have the value of x, we can use it to get y by substituting into equation 1;

`\begin{gathered} 3x+y=7 \\ 3(16)+y=7 \\ 48+y=7 \\ y=7-48 \\ y=-41 \end{gathered}`

Therefore, the solution to the given system of linear equation is;

`\begin{gathered} x=16 \\ y=-41 \end{gathered}`