Question

Solve the system of equations.
3x + y = 3
x + y = 2

Answer 1

When solving system equations, we can use substitution method or elimination. Today I'm using substitution method.

First name the 2 equations.
3x + y = 3 (1)
x + y = 2 (2)

Now pick one equation and express one algebra in forms of the other.
From (2),
x = 2 - y (3)

Now substitute (3) into (1),
3(2-y) + y = 3
6 - 3y + y = 3
6 - 2y = 3
6 - 3 = 2y
y = 1.5

Now substitute y = 1.5 into (2)
x + 1. 5 = 2
x = 2 - 1.5
x = 0.5

Therefore the answer is x = 0.5 and y = 1.5

Answer 2

The solution of the system of equations is $(x,y) = \left(\frac{1}{2}, \frac{3}{2} \right)$. $\blacksquare$

How to solve a system of linear equations

There are several ways to solve this system of linear equations, the quickest and most efficient approach consists in using determinants to calculate each variable:

$x = \frac{\left[\begin{array}{cc}3&1\\2&1\end{array}\right] }{\left[\begin{array}{cc}3&1\\1&1\end{array}\right] }$

$x = \frac{3-2}{3-1}$

$x = \frac{1}{2}$

$y = \frac{\left[\begin{array}{cc}3&3\\1&2\end{array}\right] }{\left[\begin{array}{cc}3&1\\1&1\end{array}\right] }$

$y = \frac{6-3}{3-1}$

$y = \frac{3}{2}$

The solution of the system of equations is $(x,y) = \left(\frac{1}{2}, \frac{3}{2} \right)$. $\blacksquare$

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