Question

solve the system of equations and choose the correct ordered pair.

$4x + 7y = 47$
$5x - 4y = -5$

a. $(4, 7)$
b. $(4, 5)$
c. $(3, 5)$
d. $(3, 7)$

Explanation:

Step1: Use elimination method. Multiply the first equation by 4 and the second by 7 to eliminate y.

First equation: \(4(4x + 7y)=4\times47\) → \(16x + 28y = 188\)
Second equation: \(7(5x - 4y)=7\times(-5)\) → \(35x - 28y = -35\)

Step2: Add the two new equations.

\((16x + 28y)+(35x - 28y)=188+(-35)\)
\(16x + 35x + 28y - 28y = 153\)
\(51x = 153\)

Step3: Solve for x.

\(x=\frac{153}{51}=3\)

Step4: Substitute x = 3 into the first original equation to find y.

\(4\times3 + 7y = 47\)
\(12 + 7y = 47\)
\(7y = 47 - 12 = 35\)
\(y=\frac{35}{7}=5\)

Answer:

C. (3, 5)