# How do you solve the system of equations 3x+2y=12 and y=x+1?

##### 1 Answer
Nov 7, 2016

$\left(2 , 3\right)$

#### Explanation:

In solving systems of linear equations, you can use the elimination method, substitution method or graphing. Using any of these three methods would yield the same answer so it is up to you to choose which method you are most comfortable with. However in this case, I would show both the elimination and substitution method to demonstrate that regardless of the method used, you will arrive with the same solution set.

*graphing will not be done since it is difficult to show graphs using this medium and since it is difficult to determine the exact solutions if the values are not whole numbers

$3 x + 2 y = 12$
$y = x + 1$

Substitution Method
Since $y$ is already isolated in the second equation we can use that value, to substitute for $y$ in the first equation.

$3 x + 2 \left(x + 1\right) = 12$
$3 x + 2 x + 2 = 12$
$5 x = 12 - 2$
$5 x = 10$
$x = 2$

Substitute the computed value of $x$ to the second equation to determine the value of $y$.

$y = 2 + 1$
$y = 3$

Elimination Method
$3 x + 2 y = 12$
$x - y = - 1$

Multiply the second equation by 2 to eliminate $x$ or you can also multiply the second equation by 3 to eliminate $y$. However since it is easier to multiply by 2, I will follow the first method.

$3 x + 2 y = 12$
$2 x - 2 y = - 2$

Adding the two equations eliminates the $y$ variable.

$5 x = 10$
$x = 2$

Substitute the computed value of $x$ to the second equation to determine the value of $y$.

$y = 2 + 1$
$y = 3$

Solution Set: $\left(2 , 3\right)$