How to Solve a 2-Variable Linear System and Find x+y

Question

Solve the system of linear equations: $2x + 3y = 7$, $x - y = 1$. Then find the value of $x + y$?

Accepted Answer

3

Answer

Step 1: Rearrange the second equation to express one variable in terms of the other. From $x - y = 1$, we get $x = y + 1$. Step 2: Substitute $x = y + 1$ into the first equation $2x + 3y = 7$. This gives $2(y + 1) + 3y = 7$. Step 3: Expand and simplify the substituted equation: $2y + 2 + 3y = 7$, combine like terms to get $5y + 2 = 7$. Subtract 2 from both sides: $5y = 5$, then divide by 5 to find $y = 1$. Step 4: Substitute $y = 1$ back into $x = y + 1$ to find $x$: $x = 1 + 1 = 2$. Step 5: Calculate $x + y$: $2 + 1 = 3$. Alternative shortcut: Add the two original equations directly: $(2x + 3y) + (x - y) = 7 + 1$, which simplifies to $3x + 2y = 8$. Wait, instead, add the equations after adjusting: Multiply the second equation by 2: $2x - 2y = 2$, subtract from first equation: $5y=5$, $y=1$, then find $x=2$, sum to 3. Or directly add the two original equations and rearrange: $3x + 2y = 8$, but we can also compute $x+y$ by solving for $x$ and $y$ as above.