Question

If (a,2) is the point of intersection of the straight lines $y=2x-4$ and $y=x+c$, then the value of c is equal to

• A. -1
• B. 3
• C. -2
• D. -3
• E. 1

Hint:

Algebra Tip: You don't need to set the equations equal to each other ($2x - 4 = x + c$) first. Since you already know $y=2$, plugging it in immediately turns a system of equations into basic arithmetic!

Answer 1

The Correct Option is A

Concept:
The point of intersection between two or more lines is a coordinate pair $(x, y)$ that perfectly satisfies the equations of all intersecting lines. By substituting the known coordinates of the point into the equations, we can systematically solve for any missing variables.

Step 1: Identify the intersection point.
We are given that the intersection point is $(x, y) = (a, 2)$. This means the $y$-coordinate is permanently known to be $2$.

Step 2: Substitute into the first equation to find a.
The first line is $y = 2x - 4$. Plug in $y = 2$ and $x = a$: $$2 = 2a - 4$$

Step 3: Solve for the variable a.
Add $4$ to both sides of the equation: $$6 = 2a$$ $$a = 3$$ The full point of intersection is now known: $(3, 2)$.

Step 4: Substitute the full point into the second equation.
The second line is $y = x + c$. Plug in the known intersection coordinates $x = 3$ and $y = 2$: $$2 = 3 + c$$

Step 5: Solve for the variable c.
Subtract $3$ from both sides to isolate $c$: $$c = 2 - 3$$ $$c = -1$$ Hence the correct answer is (A) -1.