Given that 𝑥 plus two, negative 10 is equal to zero, 𝑦 minus six, find the value of 𝑥 plus four 𝑦.
If the two ordered pairs given are equal, their individual components must be equal. This means that 𝑥 plus two must be equal to zero and negative 10 is equal to 𝑦 minus six. To solve the first equation, we subtract two from both sides. This gives us a value of 𝑥 equal to negative two. To solve the second equation, we add six to both sides. Negative 10 plus six is equal to negative four. So our value for 𝑦 is negative four.
Our final step is to substitute these values into the expression 𝑥 plus four 𝑦. This is equal to negative two plus four multiplied by negative four. Using our order of operations, we multiply four by negative four first. This leaves us with negative two minus 16. Subtracting 16 from negative two gives negative 18. This is the value of 𝑥 plus four 𝑦.