# How do you solve 2x + 3y = 6 and x + y = 3 using substitution?

Mar 23, 2018

$x = 3 , y = 0$

#### Explanation:

$2 x + 3 y = 6$

$x + y = 3$

Let's solve for $x$ in the second equation

$x = 3 - y$

Now let's plug $\left(3 - y\right)$ in for $x$ in the first equation

$2 \left(3 - y\right) + 3 y = 6$

$6 - 2 y + 3 y = 6$

$y = 0$

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Now we have $y$, let's find $x$

$x = 3 - y$

$x = 3 - 0$

$x = 3$

$\cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot$

Let's double check our work and use our $x$ and $y$ values in the first equation and solve it. If our numbers are correct, the equation should equal $6$

#2(3) + 3(0)

$6 + 0$

$6 = 6$! We were right!