{:[y-5=x],[x+2y=22]:} Which ordered pair (x,y) satisfies the given system of equations? Choose 1 answer: (A) (1,6) (B) (4,9) (c) (6,8) (D) (12,17)

Expressing x in terms of y: First, we can express x from the first equation: x = y - 5 Now we have x in terms of y, which we can substitute into the second equation.Substituting x into the second equation: Substitute x = y - 5 into the second equation: (y - 5) + 2y = 22 Now, let's solve for y.Solving for y: Combine like terms: 3y - 5 = 22 Add 5 to both sides: 3y = 27 Now, divide by 3 to find y: y = 27 / 3 y = 9Finding x using the first equation: Now that we have y, we can find x using the first equation: x = y - 5 x = 9 - 5 x = 4Checking the solution: We have found the solution to the system of equations: x = 4, y = 9 Now we need to check which answer choice matches our solution.Correct answer: Checking the answer choices, we see that: (A) (1,6) does not match our solution. (B) (4,9) matches our solution. (C) (6,8) does not match our solution. (D) (12,17) does not match our solution. Therefore, the correct answer is (B) (4,9).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

{:[y-5=x],[x+2y=22]:}
Which ordered pair
(x,y) satisfies the given system of equations?
Choose 1 answer:
(A)
(1,6)
(B)
(4,9)
(c)
(6,8)
(D)
(12,17)

$y-5=x$ $\newline$ $x+2 y=22$ $\newline$ Which ordered pair $(x, y)$ satisfies the given system of equations? $\newline$ Choose $1$ answer: $\newline$ (A) $(1,6)$ $\newline$ (B) $(4,9)$ $\newline$ (C) $(6,8)$ $\newline$ (D) $(12,17)$

View step-by-step help

Full solution

y-5=x

\newline

x+2 y=22

\newline

Which ordered pair

(x, y)

satisfies the given system of equations?

\newline

Choose

1

answer:

\newline

(A)

(1,6)

\newline

(B)

(4,9)

\newline

(C)

(6,8)

\newline

(D)

(12,17)

Expressing $x$ in terms of $y$ : First, we can express $x$ from the first equation: $\newline$ $x = y - 5$ $\newline$ Now we have $x$ in terms of $y$ , which we can substitute into the second equation.
Substituting $x$ into the second equation: Substitute $x = y - 5$ into the second equation: $\newline$ $(y - 5) + 2y = 22$ $\newline$ Now, let's solve for $y$ .
Solving for y: Combine like terms: $\newline$ $3y - 5 = 22$ $\newline$ Add $5$ to both sides: $\newline$ $3y = 27$ $\newline$ Now, divide by $3$ to find y: $\newline$ $y = \frac{27}{3}$ $\newline$ $y = 9$
Finding x using the first equation: Now that we have y, we can find x using the first equation: $\newline$ x = y - $5$ $\newline$ x = $9$ - $5$ $\newline$ x = $4$
Checking the solution: We have found the solution to the system of equations: $\newline$ $x = 4$ , $y = 9$ $\newline$ Now we need to check which answer choice matches our solution.
Correct answer: Checking the answer choices, we see that: $\newline$ (A) $(1,6)$ does not match our solution. $\newline$ (B) $(4,9)$ matches our solution. $\newline$ (C) $(6,8)$ does not match our solution. $\newline$ (D) $(12,17)$ does not match our solution. $\newline$ Therefore, the correct answer is (B) $(4,9)$ .