Question

Solve and check the following system:
X +2y =4
2x - y =3

Answer 1

Step-by-step explanation:

$x + 2y = 4$

$2x - y = 3$

To solve this system of equation, let's multiply the second equation by two so both equations have a $2y$:

$x + 2y = 4$

$4x - 2y = 6$

Next, let's add the two equations together to remove the $y$ and solve for $x$:

$(x + 2y) + (4x - 2y) = 4 + 6$

$5x = 10$

$x = 2$

Now that we have the value of $x$, we can plug it into either of the equations to solve for $y$:

$x + 2y = 4$

$(2) + 2y = 4$

$2y = 2$

$y = 1$

or

$2x - y = 3$

$2(2) - y = 3$

$4 - y = 3$

$y = 1$

Therefore, the solution to this system of equations is $(2, 1)$.

Answer 2

The solution of the given system of equation is x = 2 and y = 1

Step-by-step explanation:

Given,

x+2y = 4 -------eq 1

2x -y = 3 ------- eq 2

To find the value of x and y

Putting y = 2x-3 from eq 2 in eq 1 we get,

x+2(2x-3) = 4

or, x+4x-6 = 4

or, 5x = 10

or, x = 2

Again,

From eq 2 we get,

y = 2×2-3 = 1

Hence,

x = 2 and y = 1

Checking:

Putting the values of x=2 and y=1 in eq 1 and eq 2 we get,

2 + 2×1 = 4 and

2×2-1 = 3