Question

y = 2x - 1
y = -x + 2

Explanation:

Step1: Find intersection by solving equations

We have the system of equations:

$$
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$$

Set the two expressions for \(y\) equal to each other: \(2x - 1=-x + 2\).

Step2: Solve for \(x\)

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

Step3: Solve for \(y\)

Substitute \(x = 1\) into \(y=-x + 2\): \(y=-1 + 2=1\).

Step4: Graphical verification (optional)

For \(y = 2x-1\), when \(x = 0\), \(y=-1\); when \(x = 1\), \(y = 1\).
For \(y=-x + 2\), when \(x = 0\), \(y = 2\); when \(x = 1\), \(y = 1\).
Plotting these points on the grid, the lines intersect at \((1,1)\).

Answer:

The solution to the system of equations (the intersection point of the two lines) is \((1,1)\)