Question - Finding the Intersection Point of Two Lines
Solution:
To find the point at which the two lines represented by the equations intersect, you can utilize the method of substitution or elimination. In this case, substitution seems straightforward as the first equation is already solved for y. Here is how you do it:You have the following two equations:1) $$ y = 2x - 8 $$2) $$ x + y = 19 $$Substitute the expression from the first equation for y in the second equation:$$ x + (2x - 8) = 19 $$Combine like terms:$$ 3x - 8 = 19 $$Add 8 to both sides to isolate the term with $$ x $$:$$ 3x = 27 $$Divide by 3 to solve for $$ x $$:$$ x = 9 $$Now that we have the value of $$ x $$, we can plug it back into the first equation to find the corresponding value of $$ y $$:$$ y = 2(9) - 8 $$$$ y = 18 - 8 $$$$ y = 10 $$Therefore, the point of intersection for the two lines is at the coordinates (9, 10).
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