Answer:
C. X=10 and y=3
Step-by-step explanation:
Let's start by saying the first number is x and the second number is y. Now, rewrite the word problem, making sure any numbers in written form are in number form:
- 3 times x added to y is 33. x added to 3 times y is 19.
Now, translate the operations into how we usually see them in equations, e.g. "added to" as +:
[tex]3x + y = 33[/tex]
[tex]x + 3y = 19[/tex]
From here on, it's just solving systems of equations, baby!
- Multiply one of the equations by 3 so that the x's and y's can cancel out. it doesn't really matter which, but I'll go with the first one.
[tex]9x + 3y = 99[/tex]
[tex]x + 3y = 19[/tex]
- Subtract one equation from the other. (Tip: look for the equation with the larger coefficient for x so it ends up positive!)
[tex]8x = 80[/tex]
[tex] \frac{8x}{8} = \frac{80}{8} [/tex]
[tex]x = 10[/tex]
- Plug x back in one of the equations from the original system. Either works! Now, solve for y.
[tex]x + 3y = 19[/tex]
[tex]10 + 3y = 19[/tex]
[tex]3y = 19 - 10 = 9[/tex]
[tex] \frac{3y}{3} = \frac{9}{3} [/tex]
[tex]y = 3[/tex]
