Solving System of Linear Equations
The problem requires finding the coordinate pair $(x, y)$ that satisfies both linear equations simultaneously:
- Equation 1: $y = 3x - 4$
- Equation 2: $y = -x + 2$
We can solve this system by equating the expressions for $y$ from both equations, a method known as substitution.
Calculating the Intersection Point
- Set equations equal:
Since both expressions equal $y$, we can set them equal to each other:
$3x - 4 = -x + 2$
- Solve for $x$:
Rearrange the equation to isolate $x$. Add $x$ to both sides:
$3x + x - 4 = 2$
$4x - 4 = 2$
Add 4 to both sides:
$4x = 2 + 4$
$4x = 6$
Divide by 4:
$x = \frac{6}{4}$
Simplify the fraction:
$x = \frac{3}{2} \text{ or } x = 1.5$
- Solve for $y$:
Substitute the calculated value of $x = 1.5$ into either of the original equations. Using Equation 2 ($y = -x + 2$):
$y = -(1.5) + 2$
$y = -1.5 + 2$
$y = 0.5$
- Final Solution:
The solution is the point where the two lines intersect, which is $(x, y)$.
Solution: $(1.5, 0.5)$
Similar Questions
- If $P + Q = 2R$ and $R + S = 2P$, then:
The sum of two numbers is 40 and their difference is 4. What is the product of the numbers?
If 3x - ky + 8 = 0 and 9x - 18y + 20 = 0 have no solution, find k.
If \(3x-ky+8 = 0\) and \(9x-18y+20 = 0\) have no solution, find k.
Important Questions from Linear Equation in 2 or more Variables
Six years ago, the ratio of ages of A to B was 7 ∶ 5. After 4 years from now, the ratio of their ages will be 11 ∶ 9. What is A’s age at present?
7p - [3q - {8p - (4q - 10p)}] = ?
Surya is 25 years older than his son. In 5 years, he will be twice as old as his son. What will be Surya’s age after 3 years?
The difference between the ages of two sisters is 2 years when father’s age is 52. Father is elder by 2 years to mother. Elder sister’s age is half of mother’s age. Find the age of younger sister?
The sum of the digits of a 2 digit number is 9, When 27 is added to the number, the digits get interchanged. Find the number.
A. 45
B. 36
C. 18
D. 27
