Solve the following systems of equations: System 1: 2x + y = 7 x + y = 5 System 2: 2x + y = 7 x + y = 2

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for the systems of equations:

System 1:

\begin{cases} 2x + y = 7 \quad &(1) \\ x + y = 5 \quad &(2) \end{cases}

Subtract equation (2) from equation (1) to eliminate $y$ .
$(2x + y) - (x + y) = 7 - 5 \\ 2x + y - x - y = 2 \\ x = 2$
Substitute $x = 2$ into equation (2).
$x + y = 5 \\ 2 + y = 5 \\ y = 5 - 2 \\ y = 3$
The solution for the first system is $\boxed{x=2, y=3}$ .

System 2:
$\begin{cases} 2x + y = 7 \quad &(3) \\ x + y = 2 \quad &(4) \end{cases}$
Subtract equation (4) from equation (3) to eliminate $y$ .
$(2x + y) - (x + y) = 7 - 2 \\ 2x + y - x - y = 5 \\ x = 5$
Substitute $x = 5$ into equation (4).
$x + y = 2 \\ 5 + y = 2 \\ y = 2 - 5 \\ y = -3$
The solution for the second system is $\boxed{x=5, y=-3}$ .

Answer