Solve Equations Using Graphs

How many solutions does the graph have?

• One solution

• No solution

• Infinite solutions

Solve:
y=8x+1
y=6x+3

• (1, 9)

• (4, 14)

• (0, 1)

• (2, 4)

What does
"solution to a system of equations"
mean?

• It's the point where both equations equal zero

• It's the point where graphs of both equations cross the y-axis

• It's the point that solves both equations at the same time

• It's the point where graphs of both equations cross the x-axis

What is the solution to this system?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

The graph of the linear equation in two variables y = mx is _____

• a line parallel to x - axis 

• a line parallel to y - axis 

• a line passes through the origin

• not a straight line

Identify the nature of solution from the graph given.

• Consistent and unique solution

• Inconsistent : No solution

^{What is the solution?} 

• 1

• -2

• (1, 2)

• (1, -1)

Choose the correct equation for the given graph.

• y = x + 2

• y = 4 + x

• y = x - 2

• y = 4 - x

Answer explanation

As we can see in the graph that the line is intersecting x axis at 2 and y axis at -2. So here we have got two points (2, 0) and (0, -2). Now let's substitute these points in y = x - 2 (2, 0) In LHS, y = 0 In RHS, x - 2 = 2 - 2 = 0 So, LHS = RHS (0, -2) In LHS, y = -2 In RHS, x - 2 = 0 -2 = -2 So, LHS = RHS Therefore, The graph in the figure is of the equation y = x - 2 and option 3 is the correct answer.

What is the solution? 

• 1

• -2

• (1, 2)

• (1, -1)

When you graph the exact same equation twice,

• you will have no solution. 

• you will have one solution.

• you will have infinite solutions. 

• you will graph a giraffe.