Graphing
y=x-4
x+2y=4
and find that lines intersect at (4,0)
so x=4
y=0
x-y+3=0
2y-x=4
x=10
y=7
6x+2y=5
4x+y=3
x=1/2
y=1
2y-3x=-16
10x+4y-1=2x-5
x=2
y=-5
3y+4x=y+9
4x-6y=5
x=2
y=1/2
5x+6y=8
3x+4y=4
x=4
y=-2
In what ways can solving two variable systems by graphing be easier/more optimal than solving algebraically (with substitution or elimination)?
Just a sample response, but any good answer will get points.
A situation where isolating a variable and plugging back in involves a lot of fractions and ugly distributing, 5x+3y=16 and 2x+9y=18. Easier to graph than try to solve algrebraically.
Also when the system requires several operations to be performed on both equations to cancel a variable, making elimination tedious and easy to mess up on. Ie. 4x+5y=11 and 3x-2y=2.
What might some tells be when looking at a system of equations problem that substitution would be a fast and efficient method, and more ideal than others
When one of the variables in an equation already has a coefficient of 1. Just a sample answer
When might elimination be more useful to work with over graphing and substitution?
An idea is when the difference between the two coefficients for the same variable is 1.
When the coefficients are of a variable are all multiples of each other. Sample answers