Respuesta :
Let x be price of one apple and y be price of one orange.
Upon using our given information we will get a system of equation as:
[tex]5x+4y=10..(1)[/tex]
[tex]5x+5y=11..(2)[/tex]
Since we know that a system of equation will have a unique solution if,
[tex]\frac{a_1}{a_2}\neq\frac{b_1}{b_2}[/tex], where [tex]a_1[/tex] and [tex]b_1[/tex] are coefficients of x and y terms of our one equation respectively; [tex]a_2[/tex] and [tex]b_2[/tex] are coefficients of x and y terms of our second equation respectively.
Let us check that our system of equations is solvable or not.
[tex]\frac{5}{5}\neq\frac{4}{5}[/tex]
[tex]1\neq\frac{4}{5}[/tex]
We can see that our system of equation is solvable and will have a unique solution.
We will use substitution method to solve our system of equations.
Upon substituting [tex]5x=11-5y[/tex] in 1st equation we will get,
[tex]11-5y+4y=10[/tex]
Upon combining like terms we will get,
[tex]-5y+4y=10-11[/tex]
[tex]-y=-1[/tex]
Multiplying both sides of our equation by -1 we will get,
[tex]y=1[/tex]
Therefore, price of one orange is $1.
Now let us substitute y=1 in 1st equation.
[tex]5x+4\cdot 1=10[/tex]
[tex]5x+4=10[/tex]
[tex]5x=10-4[/tex]
[tex]5x=6[/tex]
[tex]x=\frac{6}{5}[/tex]
[tex]x=1.2[/tex]
Therefore, price of one apple is $1.2.
Answer:
Apple cost 1.20 and orange 1.00
Step-by-step explanation:
