Question

Solve the pair of equations $x+2y=9$ and $2x-y=8$ by graphical method.

Answer 1

Solving simultaneous equations involves using algebra to eliminate one variable and solve for the other, then using that one to find the value of the other. The solution is $x=3.33,y=2.33$.

Explanation:

Let's label our two equations as (1) and (2) to make them easy to refer to:

$2x-y=8$ (1)
$x+2y=9$ (2)

Multiply (2) by 2:

$2x+4y=18$

Subtract (1) from this equation:

$2x+4y=18$ minus
$2x-y=8$

Yields:

$3y=10$

This is an equation in only one variable, so we can solve it:

$y=\frac{10}{3}\text{or}3.33$

Substitute this in either (1) or (2) to find $x$. I'll use (2) because it's simpler:

$x+2\left(\frac{10}{3}\right)=9$

Rearranging:

$x=9-\frac{20}{3}=2.33$

The solution is $x=3.33,y=2.33$

..

Explanation:

Let's label our two equations as (1) and (2) to make them easy to refer to:

$2x-y=8$ (1)
$x+2y=9$ (2)

Multiply (2) by 2:

$2x+4y=18$

Subtract (1) from this equation:

$2x+4y=18$ minus
$2x-y=8$

Yields:

$3y=10$

This is an equation in only one variable, so we can solve it:

$y=\frac{10}{3}\text{or}3.33$

Substitute this in either (1) or (2) to find $x$. I'll use (2) because it's simpler:

$x+2\left(\frac{10}{3}\right)=9$

Rearranging:

$x=9-\frac{20}{3}=2.33$

The solution is $x=3.33,y=2.33$.