Question

solve the system of equations and choose the correct ordered pair.
$3x + 2y = 12$
$6x + 3y = 21$
a. $(3, 2)$
b. $(4, 0)$
c. $(2, 3)$
d. $(4, 3)$

Explanation:

Step1: Simplify the second equation

We can simplify the second equation \(6x + 3y=21\) by dividing each term by 3. So we get \(2x + y = 7\), and then we can express \(y\) in terms of \(x\) as \(y=7 - 2x\).

Step2: Substitute \(y\) into the first equation

Substitute \(y = 7-2x\) into the first equation \(3x + 2y=12\). We have \(3x+2(7 - 2x)=12\).
Expand the equation: \(3x + 14-4x=12\).
Combine like terms: \(-x+14 = 12\).
Subtract 14 from both sides: \(-x=12 - 14=- 2\).
Multiply both sides by - 1: \(x = 2\).

Step3: Find the value of \(y\)

Substitute \(x = 2\) into \(y=7 - 2x\). Then \(y=7-2\times2=7 - 4 = 3\).

Answer:

C. (2, 3)