The statement (2, 4) is the intersection of the two lines, explains that the point (2,4 ) is the solution.
How is the solution to the system of equations found?
Let us consider the given equations of two lines .
-6x + 4y = 4
y = -3x + 10
Rewriting the above linear equations,
6x = 4y -4 ---(1)
3x = -y + 10 ---(2)
Multiplying equation (2) by 2,
6x = 4y -4 ---(1)
6x = -2y + 20 ---(3)
Applying subtraction (1) - (3)
6y -24 = 0
6y = 24
y = 4
Substituting the value of y in equation (1)
6x = 4y -4
6x = 16 -4
6x = 12
x = 2
- Thus, the system of equations has the solution of (x, y) as (2,4).
- Since the solutions are found by calculating the intersection point of the two lines , Option D is correct.
What are linear equations?
- An equation is said to be linear if the maximum power of the variable is consistently 1.
- Another name for it is a one-degree equation.
- A linear equation with one variable has the conventional form Ax + B = 0.
- Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line.
- Both linear equations with one variable and those with two variables exist.
- A linear equation is expressed using the linear equation formula.
- A mathematical equation resembles a balance scale with identical weights on either side.
To learn more about linear equations, refer:
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