Solving Linear Equations Graphically

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. 

What is the solution?

• One Solution

• No solution

• Infinitely Many Solutions

Solve by graphing.
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

Which of these represents point-slope form of a linear equation?

• y - y₁ = m(x - x₁)

• Ax + By = C

• y = mx + b

• y=kx

By plotting the graphs of 𝑦=𝑥−1 and 𝑦=5𝑥+7 , find the point that satisfies both equations simultaneously.

• (−2,−3)

• (−1,1)

• (1,−1)

• (−3,−2)

Plot the graphs of the simultaneous equations 𝑦=2𝑥+7 , 𝑦=2𝑥−4 , and then solve the system.

• There are infinitely many solutions as both equations represent the same line.

• 𝑥 = 1 , 𝑦 = − 2

• 𝑥 = 0 , 𝑦 = 7

• There are no solutions as both equations represent parallel lines.

By plotting the graphs of 𝑦=−2𝑥+1 and 𝑦=𝑥+4 , find the point that satisfies both equations simultaneously.

• (1, 3)

• (−3,7)

• (−1,3)

• (3, 7)

By plotting the graphs of 3𝑥+2𝑦=10 and 6𝑥+4𝑦=30,determine the pair of 𝑥- and 𝑦-coordinates that satisfies both equations simultaneously

• The point coordinates that satisfy both equations are (5, 5).

• The point coordinates that satisfy both equations are (5, 0).

• The two lines are parallel, so there is no solution.

• The two lines are coincident, so there is an infinite number of solutions.

Plot the graphs of the equations 𝑦=2𝑥+7 , 𝑦=−3𝑥−3 ,and then solve the system.

• There are infinitely many solutions as both equations represent the same line.

• 𝑥 = 2 , 𝑦 =−9

• There are no solutions as both equations represent parallel lines.

• 𝑥=−2,𝑦=3

Which of the following represents the set of solutions of the equation 𝑥=−6 ?

• all the points in the vertical line passing through (−6,4)

• all the points in the vertical line passing through (4,−6)

• all the points in the horizontal line passing through (−6,4)

• all the points in the horizontal line passing through (4,−6)