Question

solve the system of equations: y = -2x + 3 y = 5x + 31 the solution is x = , y = enter dne for both if no solution exists.

Explanation:

Step1: Set the two equations equal

Since \(y=-2x + 3\) and \(y = 5x+31\), we set \(-2x + 3=5x+31\).

Step2: Solve for \(x\)

Add \(2x\) to both sides: \(3=5x + 2x+31\), which simplifies to \(3 = 7x+31\). Then subtract 31 from both sides: \(3-31=7x\), so \(-28 = 7x\). Divide both sides by 7: \(x=\frac{-28}{7}=-4\).

Step3: Solve for \(y\)

Substitute \(x = - 4\) into \(y=-2x + 3\). Then \(y=-2\times(-4)+3=8 + 3=11\).

Answer:

\(x=-4,y = 11\)