The cost of one chapstick is $1 and one eyeliner is $2.
Step-by-step explanation:
Let,
Cost of one chapstick = x
Cost of one eyeliner = y
According to given statement;
3x+2y=7 Eqn 1
4x+5y=14 Eqn 2
Multiplying Eqn 1 by 4
[tex]4(3x+2y=7)\\12x+8y=28\ \ \ Eqn\ 3[/tex]
Multiplying Eqn 2 by 3
[tex]3(4x+5y=14)\\12x+15y=42\ \ \ Eqn\ 4[/tex]
Subtracting Eqn 3 from Eqn 4
[tex](12x+15y)-(12x+8y)=42-28\\12x+15y-12x-8y=14\\7y=14[/tex]
Dividing both sides by 7
[tex]\frac{7y}{7}=\frac{14}{7}\\y=2[/tex]
Putting y=2 in Eqn 1
[tex]3x+2(2)=7\\3x+4=7\\3x=7-4\\3x=3[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{3}{3}\\x=1[/tex]
The cost of one chapstick is $1 and one eyeliner is $2.
Keywords: linear equation, elimination method
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