If we want to solve a mathematical problem it should not matter what method we choose. As long as we are correct in our reasoning, we should always end up with the same solution. This is also true for solving a system of linear equations.
In other words, solving a system of linear equations by graphing should give us the same solution as solving by substitution. Let's make sure by solving an example system.
Example
Let's consider a system of linear equations.
y=2x-4 y=- 4x+2
We can start by solving the system by graphing. To do so, let's identify the slope and the y-intercept of each equation.
Equation
Slope
Y-intercept
y= 2x+( -4)
2
-4
y= -4x+ 2
-4
2
Now we will start drawing each line at its y-intercepts. Then we will find another point that lies on each line using its slope.
We can see that the lines intersect at (1,-2). Therefore x=1 and y=-2 is the solution to the system. Let's check if we obtain the same solution using substitution. Since both equations are solved for y, we can substitute the right-hand side of Equation 1 for y in Equation 2.
