Question

Determine whether the ordered pair is the solution to the system: $\left\{\begin{array}{l}y>4x-2\\ 4x-y<20\end{array}\right.$

$a\left)\right(-2,1)$

$b\left)\right(4,-1)$

Short answer

The ordered pair $(-2,1)$is a solution to the system of inequalities $\left\{\begin{array}{l}y>4x-2\\ 4x-y<20\end{array}\right.$

And the ordered pair $(4,-1)$ is not a solution to the system of inequalities $\left\{\begin{array}{l}y>4x-2\\ 4x-y<20\end{array}\right.$

Step-by-step solution

Part a) Step 1. Given

The system of inequalities, $\left\{\begin{array}{l}y>4x-2\\ 4x-y<20\end{array}\right.$

$(x,y)=(-2,1)$

$(x,y)=(4,-1)$

Part a) Step 2. Substitute the points in the first equation

Substitute the point $(-2,1)$in the system of inequalities.

$y>4x-2$

$\left(1\right)>4(-2)-2$

$1>-10$ holds true.

Part a) Step 3. Substitute the points in the second equation

Substitute the point $(-2,1)$in the system of inequalities.

$4x-y<20$

localid="1644484036783" $4(-2)-\left(1\right)<20$

$-9<20$holds true.

The ordered pair $(-2,1)$made both the inequality true.

Therefore, $(-2,1)$is a solution to this system.

Part b) Step 1. Substitute the points in the first equation

Substitute the point $(4,-1)$in the system of inequality

$y>4x-2$

$(-1)>4\left(4\right)-2$

$-1>14$ is false

Part b) Step 2. Substitute the points in the second equation

Substitute the point $(4,-1)$in the system of inequalities.

$4x-y<20$

$4\left(4\right)-(-1)<20$

$16+1<20$

$17<20$is true

The ordered pair $(4,-1)$made one inequality true, but the other one is false.

Therefore, $(4,-1)$is not a solution to this system.