What is the answer to 4x+y=2? Does it go through the point (1,1)?
Understand the Problem
The question is asking about a line represented by the equation 4x+y=2 and whether it passes through the point (1,1). We need to check if substituting x=1 and y=1 satisfies the equation.
Answer
No, the point (1,1) does not lie on the line.
Answer for screen readers
The point (1,1) does not lie on the line represented by the equation $4x + y = 2$.
Steps to Solve
- Substituting the values into the equation
We need to check if the point (1,1) satisfies the equation $4x + y = 2$.
Substituting $x = 1$ and $y = 1$ into the equation gives: $$ 4(1) + 1 = 2 $$
- Calculating the left side
Now we calculate the left side of the equation: $$ 4(1) + 1 = 4 + 1 = 5 $$
- Comparing the results
Now, we compare the result of our calculation to the right side of the original equation: $$ 5 \neq 2 $$
Since $5$ does not equal $2$, the point (1,1) does not satisfy the equation.
The point (1,1) does not lie on the line represented by the equation $4x + y = 2$.
More Information
When checking if a specific point is on a line given by an equation, substituting the point's coordinates into the equation can quickly tell you if they satisfy it or not.
Tips
- A common mistake is to incorrectly perform the arithmetic when substituting values, leading to an incorrect conclusion. Always double-check your calculations.
