Question

PLZ HELP ASAP GIVING BRAINLIEST

Answer 1

The first  system of equations has a solution point at (8,2)

The second system of equations has a solution point at (5,0)

The third system of equations has a solution point at (-1,2)

The fourth system of equations has a solution point at (5,3)

Why?

Solving each systems of equations by the elimination method, we have:

First equation:

$\left \{ {{2x-2y=12} \atop {-2x-3y=-22}} \right.$

Adding the equations, we have:

$(2x-2x)+(-2y-3y)=12-22\\\\0-5y=-10\\\\y=2$

Now, subtituting "y" into the first equation, we have:

$2x-2*2=12\\\\2x=4+12\\\\x=\frac{16}{2}=8$

We have that the first system of equations has a solution point at (8,2)

Second equation:

$\left \{ {{2x-6y=10} \atop {x+8y=5}} \right$

Multiplying the second equation by -2 and adding it to the first equation, we have:

$\left \{ {{2x-6y=10} \atop {x*(-2)+8y*(*-2)=5*(*2)}} \right\\\\\left \{ {{2x-6y=10} \atop {-x-16y=-10}} \right\\\\(2x-2x)+(-5y-16y)=10-10\\\\0-21y=0\\\\y=0$

Now, subtituting "y" into the first equation, we have:

$2x-6*0=10\\\\x=\frac{10}{2}=5$

We have that the second system of  equations has a solution point at (5,0)

Third equation:

$\left \{ {{3x-y=-5} \atop {x+4y=7}} \right$

Multiplying the second equation by -3 and adding it to the first equation, we have:

$\left \{ {{3x-y=-5} \atop {x*(-3)+4y*(*-3)=7*(-3)}} \right\\\\\left \{ {{3x-y=-5} \atop {-3x-12y=-21}} \right\\\\(3x-3x)+(-y-12y)=-5-21\\\\-13y=-26\\\\y=\frac{26}{13}=2$

Now, subtituting "y" into the first equation, we have:

$3x-2=-5\\\\3x=-5+2\\\\x=\frac{-3}{3}=-1$

We have that the third system of equations has a solution point at (-1,2)

Fourth equation:

$\left \{ {{x-y=2} \atop {2x+y=13}} \right$

Multiplying the first equation by -2 and adding it to the first equation, we have:

$\left \{ {{x*(-2)-y*(-2)=2*(-2)} \atop {2x+y=13}} \right\\\\\left \{ {{-2x+2y=-4} \atop {2x+y=13}} \right\\\\(-2x+2x)+(2y+y)=-4+13\\\\0+3y=9\\\\y=\frac{9}{3}=3$

Now, subtituting "y" into the first equation, we have:

$x-3=2\\\\x=2+3\\\\x=5$

We have that the fourth system of equations has a solution point at (5,3)

Have a nice day!