Question

solve the following system of equations. express your answer as an ordered pair in the format (a,b), with no spaces between the numbers or symbols. $3x + 4y = 17$ $-4x - 3y = -18$

Explanation:

Step1: Multiply equations to eliminate a variable

Multiply the first equation \(3x + 4y = 17\) by 4: \(12x + 16y = 68\)
Multiply the second equation \(-4x - 3y = -18\) by 3: \(-12x - 9y = -54\)

Step2: Add the two new equations

Add \(12x + 16y = 68\) and \(-12x - 9y = -54\):
\((12x - 12x) + (16y - 9y) = 68 - 54\)
\(7y = 14\)

Step3: Solve for \(y\)

Divide both sides by 7: \(y = \frac{14}{7} = 2\)

Step4: Substitute \(y = 2\) into first equation

Substitute into \(3x + 4y = 17\):
\(3x + 4(2) = 17\)
\(3x + 8 = 17\)

Step5: Solve for \(x\)

Subtract 8: \(3x = 17 - 8 = 9\)
Divide by 3: \(x = \frac{9}{3} = 3\)

Answer:

(3,2)