Ans: $4/10$ 8. Solve the following system of linear equations: $$3x + y = 10$$ $$x - y = 2$$ Ans: $$x=3$$ $$y=1$$ (system of equations, linear equations, substitution method, elimination method)

Step 1: Add the two equations

We have two linear equations. We can solve this system using the elimination method. Notice that the coefficients of $y$ are $+1$ and $-1$. Adding the two equations will eliminate the $y$ variable, allowing us to solve for $x$.

Step 2: Simplify and solve for x

After adding the equations, the $y$ terms cancel out, leaving us with an equation involving only $x$. We then simplify this equation to find the value of $x$.

Step 3: Substitute x into an equation

Now that we have the value of $x$, we can substitute it into either of the original equations to find the value of $y$. Let's use the first equation, $3x + y = 10$.

Step 4: Solve for y

By substituting $x=3$ into the first equation, we get $9 + y = 10$. Subtracting $9$ from both sides gives us the value of $y$.

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