𝑃 is the point of intersection of the lines with equations 𝑥−𝑦+1=0 and 𝑥+2𝑦−11=0Write down the coordinates of 𝑃.powered byOxyx−y+1=0x+2y−11=0P
Question
𝑃 is the point of intersection of the lines with equations
and
Write down the coordinates of 𝑃.
powered by
Oxy
P
Solution
To find the point of intersection P of the two lines, we need to solve the system of equations given by the two lines. The system of equations is:
- x - y + 1 = 0
- x + 2y - 11 = 0
Step 1: Rearrange equation 1) to solve for x: x = y - 1
Step 2: Substitute x in equation 2) with y - 1: (y - 1) + 2y - 11 = 0
Step 3: Simplify the equation to solve for y: 3y - 12 = 0
Step 4: Solve for y: y = 12 / 3 = 4
Step 5: Substitute y = 4 in equation 1) to solve for x: x = 4 - 1 = 3
So, the point of intersection P of the two lines is (3, 4).
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