Solve simultaneous linear equations by plotting their graphs and finding the point of intersection.
A linear equation like y=mx+c forms a straight line when plotted, found by calculating y for a few values of x.
For y=2x+1, find y when x=0 and x=2.
x=0: y=1; x=2: y=5
For x+y=6, find two points on this line.
x=0,y=6 and x=6,y=0 are both solutions
The solution to two simultaneous equations is the point where their graphs intersect — this point satisfies both equations.
Two lines y=x+2 and y=−x+6 intersect where?
Setting equal: x+2=−x+6 → 2x=4 → x=2, y=4; intersection is (2,4)
Why does the intersection point solve both equations simultaneously?
Because it's the only point that lies on both lines, meaning its coordinates satisfy both equations at once
1. For y=3x−1, find y when x=0 and x=1.
2. Find two points on the line 2x+y=8.
3. Two lines y=2x and y=x+3 intersect where?
4. Two lines x+y=10 and x−y=2 intersect where?
5. If two lines are parallel, how many solutions does the simultaneous system have?