How do you solve x+y=3; x+2y=5?

Apr 7, 2015
• We can solve for the values of x and y using the 'Elimination by Substitution' method.

• Let's number the equations first:
$x + y = 3$ ------(1)
$x + 2 y = 5$------(2)

In (1), by transposing $y$ to the other side, we get
$x = 3 - y$
Substituting this value of $x$ in (2), we get
$\left(3 - y\right) + 2 y = 5$
$3 + y = 5$
$y = 5 - 3$
$y = 2$
Here, we eliminated $x$ by substituting its value in (2)

• We Substitute this value of $y$ in (1) to get
$x + 2 = 3$
$x = 3 - 2$
$x = 1$

• The Solution for the equations (1) and (2) is:
$x = 1 , y = 2$

• Once we arrive at a solution, it is a good idea to VERIFY our answer

Substituting $x = 1 , y = 2$ in (1) we get
Left Hand Side: $x + y = 1 + 2 = 3$(Right Hand Side)

Substituting $x = 1 , y = 2$ in (2) we get
Left Hand Side: $x + y = 1 + \left(2 \cdot 2\right) = 5$(Right Hand Side)

We have verified our answer, and we can be sure that it's correct.