Answer
Price of a TV $=\$350$.
Price of a stereo $=\$370$.
Work Step by Step
Step 1:- Assume unknown quantities as variables.
Let the price of the TV $=x$.
Let the price of the stereo $=y$.
Step 2:- Write system of equations.
The given values are
$3$ TV $+ 4$ stereo $= \$2530$
$4$ TV $+ 3$ stereo $= \$2510$
Or we can write.
$\Rightarrow 3x+4y=2530$ ...... (1)
$\Rightarrow 4x+3y=2510$ ...... (2)
Step 3: Solve the system of equations.
Multiply equation (1) by $4$ and equation (2) by $-3$.
$\Rightarrow 12x+16y= 10120$ ...... (3)
$\Rightarrow -12x-9y=-7530$ ...... (4)
Add equation (3) and (4).
$\Rightarrow 12x+16y-12x-9y=10120-7530$
Simplify.
$\Rightarrow 7y=2590$
Divide both sides by $7$.
$\Rightarrow \frac{7y}{7}=\frac{2590}{7}$
Simplify.
$\Rightarrow y=370$
Plug the value of $y$ into equation (1).
$\Rightarrow 3x+4(370)=2530$
Simplify.
$\Rightarrow 3x+1480=2530$
Isolate $x$.
$\Rightarrow x=\frac{2530-1480}{3}$
Simplify.
$\Rightarrow x=350$.
Step 4: Check the answers.
Substitute the values of $x$ and $y$ into equation (2).
$\Rightarrow 4(350)+3(370)=2510$
$\Rightarrow 1400+1110=2510$
$\Rightarrow 2510=2510$. True.
