Determine Whether a Point Is a Solution System

How can you tell if a point is a solution to a system?

• It makes the first equation true.

• The (x,y) coordinates satisfy both equations

• It makes logical sense

• It makes neither equation negative

Will the solution (-3, -7) make the following system of equations a true statement? 
y = 4x + 5
y = x – 4

• YES

• NO

Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7

• yes

• no

What is the solution to this system of equations?

• (2,2)

• (0,3)

• (0,0)

• No Solution

Hint: Points on a line are in the form (x, y).

• Yes, the point (0, 4) makes both equations true.

• No, the point (0, 4) makes the top equation true but the bottom equation false.

• No, the point (0, 4) makes the bottom equation true but the top equation false.

• No, the point (0, 4) makes both equations false.

Answer explanation

The point given is (0, 4), which means x=0 and y=4. Plug these values into both equations and evaluate to see if the left hand side is equal to the right hand side of each equation.

Is (-2,4) a solution to the system?

• Solution

• Not a solution

Is the points (-4, 4) a solution to the system of equations?

• Yes

• No

Is ( 2, -1) a solution

*watch your signs*

y = -x - 3

y= 3x + 1

• Yes

• No

Is (-3, -7) a solution the system:

y = 4x + 5

y = x – 4

• YES

• NO

Is (-1,2) a solution for this system?

x=-1

y=3x+5

• yes

• no