Question

Drag the tiles to the correct boxes to complete the pairs. Match each point of intersection with the system of equations whose solution is at that point.

Answer 1

To determine which point is a solution to which equation system, you have to identfy which line corresponds to which equation and the coordinates of each point.

Points

W (≈-7/3,≈4/3)

X (-1,3)

Y (1,1)

Z (≈-1/2,-2)

The symbol ≈ indicates that is an approximate value.

Brown line

Has y-intercept at (0,-3)

And slope

Using points (0,-3) and (-1,-1)

$m=\frac{-3--1}{0--1}=-\frac{2}{1}=-2$

Its equation is y=-2x-3

Blue line

Has y-intercept (0,2)

And slope

Using points (0,2) and (-1,-3)

$m=\frac{2-3}{0--1}=-1$

Its equation is y=-x+2

Red line

Has y-intercept (0,4)

And slope

Using points (0,4) and (-1,-3)

$m=\frac{4-3}{0--1}=1$

Its equation is y=x+4

Black line

Has y-intercept (0,-1)

And slope

Using points (0,-1) and (1,1)

$m=\frac{1-(-1)}{1-0}=2$

The equation for this line is y=2x-1

The first equation system is

y=-2x-3

y=2x-1

Corresponds to the intersection between the brown and black lines. The point that is a solution for this system is Z

The second equation system is

y=x+4

y=-x+2

Corresponds to the intersection between the blue and red lines. The point that is a solution for this system is X

The third equation system is

y=-2x-3

y=x+4

Corresponds to the intersection between the brown and red lines. The point that is a solution for this system is W

The fourth equation system is

y=2x-1

y=-x+2

Corresponds to the intersection between the black and blue lines. The point that is a solution for this system is Y

Another way for solving this exercise is by calculating the solution of each system and placing the results in the grid. For example for the first system:

y=-2x-3

y=2x-1

$-2x-3=2x-1$

solve for x

$\begin{gathered} -2x-2x-3=2x-2x-1 \\ -4x-3+3=-1+3 \\ -4x=2 \\ -\frac{4x}{-4}=\frac{2}{-4} \\ x=-\frac{1}{2} \end{gathered}$

And now replace this value in one of the equations

$\begin{gathered} y=-2(-\frac{1}{2})-3 \\ y=-2 \end{gathered}$

The solution for this system is (-1/2,-2) → If you look at the coordinates determined above, you'll see that these correspond to point Z

Both ways are equally valid to determine which point corresponds to each system.