Solve the system of simultaneous equations: 1) 3x + y = 1 2) 2x − 3y = 8

Question

ScanSolve AI Tutor · Accepted Answer

To solve the system of simultaneous equations:

Multiply the first equation by 3 to make the coefficient of $y$ equal in magnitude to the second equation, allowing for elimination.
$3(3x + y) = 3(1)$ $9x + 3y = 3 \quad (*)$
Add the modified first equation $(*)$ to the second equation to eliminate $y$ .
$(9x + 3y) + (2x - 3y) = 3 + 8$ $11x = 11$
Solve for $x$ .
$x = \frac{11}{11}$ $x = 1$
Substitute the value of $x = 1$ into the original first equation ( $3x + y = 1$ ) to find $y$ .
$3(1) + y = 1$ $3 + y = 1$ $y = 1 - 3$ $y = -2$
The solution is $x = 1$ and $y = -2$ .

Comparing this with the given options:
A: $x = 1$ and $y = -2$
B: $x = -2$ and $y = -1$
C: $x = 2$ and $y = -1$
D: $x = 1$ and $y = 2$

The correct option is A.

The final answer is $\boxed{\text{A: } x = 1 \text{ and } y = -2}$ .

Answer