Question

directions: scan the qr code and watch the video to answer the questions in the first box. once you understand the concept try the practice problems. determining if each coordinate is a solution for the system. use the qr code at the bottom of the page to check your answers. video question notes 1.) is (2, 5) a solution for the system of linear equations below? 3x + 4y = 24 and 2x + 3y = 19 2.) is (2, 2) a solution for the system linear equations below? -2x + 4y = 4 and x + y 3.) is (3, 4) a solution for the system of linear equations below? y + 5 = 3x and y - 7 = -1x 4.) is (4, 0) a solution for the sys linear equations below? 5x + 4y = 20 and 3x check and correct your work. how did you do?

Explanation:

Problem 1: Is (2, 5) a solution?

Step1: Substitute into first equation

Substitute \(x = 2\), \(y = 5\) into \(3x + 4y\):
\(3(2)+4(5)=6 + 20 = 26\).
Check if \(26 = 24\)? No.
(Even if we check the second equation, since first fails, (2,5) is not a solution.)

Step1: Substitute into \(-2x + 4y\)

Substitute \(x = 2\), \(y = 2\) into \(-2x + 4y\):
\(-2(2)+4(2)=-4 + 8 = 4\).
This matches \(4\).

Step2: Substitute into \(x + y\) (Assume full equation, e.g., \(x + y = 4\) for consistency)

\(2 + 2 = 4\), which matches.
(If second equation is different, adjust, but with given \(-2x + 4y = 4\) holds, and if \(x + y = 4\), it holds. So (2,2) is a solution.)

Step1: Substitute into \(y + 5 = 3x\)

Substitute \(x = 3\), \(y = 4\):
\(4 + 5 = 9\), \(3(3)=9\). Matches.

Step2: Substitute into \(y - 7 = -x\)

\(4 - 7 = -3\), \(-1(3)=-3\). Matches.

Answer:

No

Problem 2: Is (2, 2) a solution? (Assume the second equation is \(x + y=\dots\), but let's use given \(-2x + 4y = 4\) first)