Question

question 1 20 pts which graph represents the solution to the systems of equations? y = x - 1 y = -2x + 5

Explanation:

Step1: Set the two equations equal.

Since \(y=x - 1\) and \(y=-2x + 5\), we set \(x-1=-2x + 5\).

Step2: Solve for \(x\).

Add \(2x\) to both sides: \(x+2x-1=-2x+2x + 5\), which simplifies to \(3x-1 = 5\). Then add 1 to both sides: \(3x-1 + 1=5 + 1\), so \(3x=6\). Divide both sides by 3: \(x = 2\).

Step3: Solve for \(y\).

Substitute \(x = 2\) into \(y=x - 1\), then \(y=2-1=1\).

Answer:

The solution of the system is the point \((2,1)\), so the graph with the intersection point \((2,1)\) represents the solution to the system of equations.