A system of equation in two variables consists of two linear equations of the form
ax+by=c
dx+ey=f
The solution is the ordered pair (x,y) that satisfies both equations.
Example:
2x-y=6
x+3y=10
The solution is (4,2) since the ordered pair makes both equations true.
How to Solve of Systems of Two Linear Equations by Graphing (Steps)
1. Graph the two equations using intercepts (standard form: Ax+By=C), or the slope m, and intercept b (slope intercept form y=mx+b).
2. Find the coordinates of the point of intersection of the two lines.
3. You should have one of the possible solutions
a) The two lines intersect at one point (different slope & intercept) => One solution
b) The two lines lie on top of one another (same slope & intercept) => Infinitely many solutions
c) The two lines are parallel and never intersect (same slope & different intercept) => No solutions
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