Respuesta :
The value of x and y is [tex]x=2[/tex] and [tex]y=0.5[/tex]
Step-by-step explanation:
Let x denote the sodas.
Let y denote the bags of popcorn.
Given: Kaelyn bought a soda and two bags of popcorn for $3. Writing this as equation,
[tex]x+2y=3[/tex]
Her brother bought three sodas in a bag of popcorn for $6.50. Writing this as equation,
[tex]3x+y=6.50[/tex]
Using substitution method, let us find the value of x from the equation [tex]x+2y=3[/tex] by subtracting 2y from both sides of the equation, we get,
[tex]x=3-2y[/tex]
Now, substituting the value of x in [tex]3x+y=6.50[/tex], we get,
[tex]\begin{array}{r}{3(3-2 y)+y=6.50} \\{9-6 y+y=6.50} \\{9-5 y=6.50}\end{array}[/tex]
Subtracting 9 from both sides of the equation, we get,
[tex]\begin{aligned}-5 y &=-2.5 \\y &=0.5\end{aligned}[/tex]
Now, substituting the value of [tex]y=0.5[/tex] in [tex]x=3-2y[/tex], we get
[tex]\begin{aligned}x &=3-2(0.5) \\&=3-1 \\x &=2\end{aligned}[/tex]
Thus, the value of x and y is [tex]x=2[/tex] and [tex]y=0.5[/tex]
