Question

solve the system of equations. 3x - 2y = 9 -4x + y = 3 (x, y) = (select choice, select choice)

Explanation:

Step1: Solve the second equation for y

From \(-4x + y = 3\), we can express \(y\) in terms of \(x\) by adding \(4x\) to both sides. So, \(y = 4x + 3\).

Step2: Substitute y into the first equation

Substitute \(y = 4x + 3\) into \(3x - 2y = 9\). We get \(3x - 2(4x + 3) = 9\).

Step3: Simplify and solve for x

First, expand the left - hand side: \(3x-8x - 6=9\). Combine like terms: \(-5x-6 = 9\). Add 6 to both sides: \(-5x=9 + 6=15\). Divide both sides by \(-5\): \(x=\frac{15}{-5}=-3\).

Step4: Substitute x back into the equation for y

We know that \(y = 4x+3\), and \(x=-3\). So, \(y = 4\times(-3)+3=-12 + 3=-9\).

Answer:

\((-3,-9)\)