Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Is $(2,7)$ a solution to this system of equations? $\newline$ $y = 3x + 1$ $\newline$ $y = 2x + 5$ $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

View step-by-step help

View step-by-step help

Is (x, y) a solution to the system of equations?

Full solution

Q. Is

(2,7)

a solution to this system of equations?

\newline

y = 3x + 1

\newline

y = 2x + 5

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Substitute and Check First Equation: First, we will substitute the point $(2,7)$ into the first equation and check if it holds true. The first equation is $y = 3x + 1$ . If we substitute $x=2$ and $y=7$ , we get $7 = 3 \times 2 + 1$ .
Check First Equation Result: After performing the calculation, we find that $7 = 6 + 1$ , which simplifies to $7 = 7$ . This is true. Therefore, the point $(2,7)$ satisfies the first equation.
Substitute and Check Second Equation: Next, we will substitute the point $(2,7)$ into the second equation and check if it holds true. The second equation is $y = 2x + 5$ . If we substitute $x=2$ and $y=7$ , we get $7 = 2\times 2 + 5$ .
Check Second Equation Result: After performing the calculation, we find that $7 = 4 + 5$ , which simplifies to $7 = 9$ . This is not true. Therefore, the point $(2,7)$ does not satisfy the second equation.
Final Solution Determination: Since the point $(2,7)$ does not satisfy both equations, it is not a solution to the system of equations.

More problems from Is (x, y) a solution to the system of equations?

Question

Solve using substitution.

5x - 2y = -7

x = -5

Posted 3 months ago

Question

(1,1)

a solution to this system of equations?

\newline

4x + 10y = 14

\newline

x + 6y = 7

\newline

\newline

\newline

Posted 3 months ago

Question

Which describes the system of equations below?

\newline

y = –3x + 9

\newline

y = –3x + 9

\newline

\newline

\text{(A) consistent and independent}

\newline

\text{(B) consistent and dependent}

\newline

\text{(C) inconsistent}

Posted 3 months ago

Question

Solve using elimination.

\newline

7x - 8y = -17

\newline

-7x + 3y = 2

\newline

(\_\_\_\_, \_\_\_\_)

Posted 3 months ago

Question

\newline

x = -2

\newline

-2x + 2y = -8

\newline

(\_\_\_\_, \_\_\_\_)

Posted 3 months ago

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

At a community barbecue, Mrs. Wilkerson and Mr. Hogan are buying dinner for their families. Mrs. Wilkerson purchases

3

hot dog meals and

3

hamburger meals, paying a total of

\$36

. Mr. Hogan buys

1

hot dog meal and

3

hamburger meals, spending

\$26

in all. How much do the meals cost?

\newline

Hot dog meals cost

\$

_______ each, and hamburger meals cost

\$

Posted 3 months ago

Question

Solve the system of equations by substitution.

\newline

-3x - y - 3z = -11

\newline

z = 5

\newline

x - y + 3z = 19

\newline

(____.____,____)

Posted 3 months ago

Question

Solve the system of equations by elimination.

\newline

x - 3y - 2z = 10

\newline

3x + 2y + 2z = 14

\newline

2x - 3y - 2z = 16

\newline

(\_,\_,\_)

Posted 2 months ago

Question

Solve the system of equations.

\newline

y = x^2 + 36x + 3

\newline

y = 22x - 37

\newline

Write the coordinates in exact form. Simplify all fractions and radicals.

\newline

(\_,\_)

\newline

(\_,\_)

Posted 2 months ago

Question

Solve the system of equations.

\newline

y = -x - 24

\newline

x^2 + y^2 = 488

\newline

Write the coordinates in exact form. Simplify all fractions and radicals.

\newline

(\_,\_)

\newline

(\_,\_)

Posted 3 months ago