Question

1. consider the equation 3x + 4y = 32 for the following questions.

a. is (4, 5) a solution? show your work and/or explain your reasoning.
b. is (0, 7) a solution? show your work and/or explain your reasoning.
c. is (12, -1) a solution? show your work and/or explain your reasoning.

Explanation:

Step1: Substitute x=12, y=-1

Substitute \( x = 12 \) and \( y = -1 \) into the equation \( 3x + 4y = 32 \).
Calculate \( 3(12) + 4(-1) \).

Step2: Compute the left - hand side

First, calculate \( 3(12)=36 \) and \( 4(-1)=-4 \).
Then, add them together: \( 36+(-4)=36 - 4 = 32 \).
Since the left - hand side equals the right - hand side (\( 32=32 \)) after substitution.

Answer:

Yes, \((12, - 1)\) is a solution because when we substitute \(x = 12\) and \(y=-1\) into the equation \(3x + 4y\), we get \(3\times12+4\times(-1)=36 - 4 = 32\), which is equal to the right - hand side of the equation \(3x + 4y = 32\).