Question

question
solve the system of equations using elimination: 7x - 2y = 11 and x - 3y = 7.
answer attempt 1 out of 2

Explanation:

Step1: Multiply the second equation

To eliminate \(x\), multiply the second equation \(x - 3y = 7\) by \(7\) to get \(7x - 21y = 49\).

Step2: Subtract the equations

Subtract the new second equation from the first equation: \((7x - 2y) - (7x - 21y) = 11 - 49\). Simplify to \(19y = -38\).

Step3: Solve for \(y\)

Divide both sides by \(19\): \(y = \frac{-38}{19} = -2\).

Step4: Substitute \(y\) into an equation

Substitute \(y = -2\) into \(x - 3y = 7\): \(x - 3(-2) = 7\), so \(x + 6 = 7\), then \(x = 1\).

Answer:

The solution is \(x = 1\) and \(y = -2\) (or as an ordered pair \((1, -2)\)).