Question

Solve the simultaneous equations. 2x+y=8; : y = (1 + x)/2 graphically.​

Answer 1

Step-by-step explanation:

We find three points for each equation, by choosing three values of x and computing the corresponding y values. We'll put our results in tables.

Line 1: 2x−y=1

y=2x−1

Substituting x=−1,0,1 in the above equation, we find

y=2x−1

x −1 0 1

2x −2 0 2

y=2x−1 −3 −1 1

Line 2: x+2y=8

2y=−x+8⇒y=−

2

x

+4

Substituting x=−2,0,2 in above equation, we get

y=−

2

x

+4

x −2 0 2

−

2

x

1 0 −1

y=−

2

x

+4 5 4 3

We plot the points (−1,−3), (0,−1) and (1,1) in a graph sheet and draw the line through them. Next, we plot the points (−2,5), (0,4) and (2,3) in the same graph sheet and draw the line through them. We find that the two graphs are intersecting at the point (2,3). Hence, the system of equations has only one solution (unique solution|) and the solution is x=2, y=3. Therefore the solution is (2,3).