The Graph of The Following System of Equations is −2x + y = 3 and 4x + 2y = 2. Solve this using the graph.
An equation of degree 1 is called linear equations. The standard form of linear equations in two variables is ax + by = c, where a, b and c are constants.
Answer: The solution for the system of linear equations -2x + y = 3 and 4x + 2y = 2 is (x, y) = (-0.5, 2)
Let's solve the system of linear equations in two variables.
Explanation:
The given equations are -2x + y = 3 --- (1) and 4x + 2y = 2 --- (2)
From the graph, it is clear that the intersecting point of the given two linear equations is (-0.5, 2). So, this is the solution of the given system of equations.
Let's solve the equations algebraically.
From equation (2), we get
4x + 2y = 2
x = (2 - 2y) / 4
To solve the system of linear equations, we will substitute value of x = (2 - 2y) / 4 in equation (1) and solve for x.
⇒ -2((2 - 2y) / 4) + y = 3
⇒ -4 + 4y + 4y = 12
⇒ 8y = 12 + 4
⇒ 8y = 16
⇒ y = 2
Put y = 1 in equation (2).
⇒ x = (2 - 2(2))/4 = (2 - 4)/4 = -2/4
⇒ x = -0.5
We can use Cuemath's online system of equations calculator to solve the equations.