Question

what is the solution to this system of linear equations?
5x + 6y = 29
3x + 6y = 27

a. (4, 1)
b. (1, 4)
c. (1, 7)
d. (7, 1)

Explanation:

Step1: Subtract the two equations

Subtract the second equation \(3x + 6y = 27\) from the first equation \(5x + 6y = 29\).

$$
LATEXBLOCK0
$$

Step2: Solve for x

Divide both sides of \(2x = 2\) by 2.

$$ x = \frac{2}{2} = 1 $$

Step3: Substitute x into one equation

Substitute \(x = 1\) into the second equation \(3x + 6y = 27\).

$$ 3(1) + 6y = 27\\ 3 + 6y = 27 $$

Step4: Solve for y

Subtract 3 from both sides: \(6y = 27 - 3 = 24\). Then divide by 6: \(y = \frac{24}{6} = 4\).

Answer:

B. (1, 4)