Question

use elimination to solve the system of equations.
$3x + 4y = 29$
$6x + 5y = 43$
( , )
need help?

Explanation:

Step1: Eliminate x by scaling

Multiply the first equation \(3x + 4y = 29\) by 2 to get \(6x + 8y = 58\).

Step2: Subtract the second equation

Subtract \(6x + 5y = 43\) from \(6x + 8y = 58\):
\((6x - 6x)+(8y - 5y)=58 - 43\)
\(3y = 15\).

Step3: Solve for y

Divide both sides by 3: \(y=\frac{15}{3}=5\).

Step4: Substitute y into first equation

Substitute \(y = 5\) into \(3x + 4y = 29\):
\(3x+4(5)=29\)
\(3x + 20 = 29\).

Step5: Solve for x

Subtract 20: \(3x=29 - 20 = 9\), then \(x=\frac{9}{3}=3\).

Answer:

\((3, 5)\)