Question

elimination with multiplication
question 2 of 10 (1 point) | question attemp
solve the following system of equations.
-3x + 2y = -6
5x - 4y = 16
x =

y =

Explanation:

Step1: Multiply first equation

To eliminate \(y\), multiply the first equation \(-3x + 2y=-6\) by \(2\). We get \(2\times(-3x + 2y)=2\times(-6)\), which simplifies to \(-6x + 4y=-12\).

Step2: Add to second equation

Now add this new equation \(-6x + 4y=-12\) to the second equation \(5x - 4y = 16\). So \((-6x+4y)+(5x - 4y)=-12 + 16\). Combining like terms, \(-6x+5x+4y - 4y=4\), which gives \(-x=4\), so \(x=- 4\).

Step3: Substitute \(x\) into first equation

Substitute \(x = - 4\) into the first original equation \(-3x+2y=-6\). We have \(-3\times(-4)+2y=-6\), which is \(12 + 2y=-6\).

Step4: Solve for \(y\)

Subtract \(12\) from both sides: \(2y=-6 - 12=-18\). Then divide by \(2\): \(y=\frac{-18}{2}=-9\).

Answer:

\(x = - 4\), \(y=-9\)