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
2 biscuits and 1 chocolate cost ₹69.
2 chocolates and 3 cups of coffee cost ₹127.
3 biscuits, 4 chocolates, and 2 cups of coffee cost ₹229.
Find the total cost (in ₹) of 5 biscuits, 5 chocolates, and 5 cups of coffee.
Simplify:
(4.2)3 − (1.2)3⁄(4.2)2 + 5.04 + (1.2)2If 0.4x + 0.16y = 1.7 and 0.3x + 0.12y = 3.4, then which of the following is correct?
The value of the expression (1.552 + 0.552 + 1.55 × 0.55) is equal to:
Find the value of Y, if X - 2Y + 2Z = 16, X - Y + Z = 9 and 2X - 3Y - Z = 9.
For which of the following values of a and b do the given equations have NO solution?
x − ay = 2 − a
(1 − a)x + 6y = a + b- If $P + Q = 2R$ and $R + S = 2P$, then:
The solution of the following equations is:
5x + 4y - 8z = 1
7x - 9y + z = -1
2x + 3y - 4z = 1
Solve the system: \(y = 2x + 1\) and \(y = -x + 4\).
The sum of two numbers is 40 and their difference is 4. What is the product of the numbers?
Important Questions from Linear Equation in 2 or more Variables
If \(3x+6y+9z = \dfrac{20}{3}, 6x+9y + 3z = \dfrac{17}{3}\) and \(18x+ 27y - z = \dfrac{113}{9}\) , then what is the value of \(75x+113y \ ?\)
If the system of equations 2x - 3y - 3 and -4x + qy - p/2 is inconsistent which of the following cannot be the value of p ?
If \(4x + \dfrac{6}{y}= 15 \) and \(6x - \dfrac{8}{y} = 14\) , then the value of p in y = px - 2 is :
Simplify: 7x + 3x(x – 4) = ?
A. 10x + 12
B. 10x – 12
C. 3x2 + 5x
D. 3x2 – 5xIf 5x + y = 17 and xy = 6, then what is the value of 125x3 + y3 ?
