Solve the system 8.35x − 4.52y = 9.03 and 2.49x + y = 16.83, giving each answer to two decimal places.

Step-by-step solution

1. 1

   Use the equation where a variable already has coefficient 1. In the second equation $y$ stands alone, so substitution costs nothing and avoids scaling both equations:

   $y=16.83-2.49x$

2. 2

   Substitute into the first equation.

   $8.35x-4.52\left(16.83-2.49x\right)=9.03$

   Distribute, remembering the $-4.52$ reaches both terms:

   $4.52\times 16.83=76.0716,\qquad 4.52\times 2.49=11.2548$

   $8.35x-76.0716+11.2548x=9.03$

3. 3

   Collect and solve for x.

   $19.6048x=9.03+76.0716=85.1016$

   $x=\frac{85.1016}{19.6048}=4.340855\approx 4.34$

4. 4

   Back-substitute for y. Use the unrounded $x$ to avoid compounding the rounding:

   $y=16.83-2.49(4.340855)=16.83-10.808730=6.021270\approx 6.02$

   $\boxed{x\approx 4.34,\qquad y\approx 6.02}$

5. 5

   Check in both original equations. First: $8.35(4.340855)-4.52(6.021270)=36.246-27.216=9.030$ ✓. Second: $2.49(4.340855)+6.021270=10.809+6.021=16.830$ ✓. Using the rounded $x=4.34$ instead would give $y=16.83-10.8066=6.0234$, which still rounds to $6.02$ — but keeping full precision is the safer habit.