2x-y+3 =0 and x+y-5 =0 find the point of intersect of the following pairs of lines.
Question
2x - y + 3 = 0
and
x + y - 5 = 0
find the point of intersect of the following pairs of lines.
Solution
To find the point of intersection of the two lines, we can use the method of substitution or elimination. Here, we will use the method of substitution.
Step 1: From the second equation, we can express x in terms of y: x = 5 - y
Step 2: Substitute x = 5 - y into the first equation: 2(5 - y) - y + 3 = 0
Step 3: Simplify the equation: 10 - 2y - y + 3 = 0
Step 4: Combine like terms: -3y + 13 = 0
Step 5: Solve for y: y = 13/3
Step 6: Substitute y = 13/3 into the equation x = 5 - y to find x: x = 5 - 13/3 = 2/3
So, the point of intersection of the two lines is (2/3, 13/3).
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