Answer:
(arranged from top to bottom)
System #3, where x=6
System #1, where x=4
System #7, where x=3
System #5, where x=2
System #2, where x=1
Step-by-step explanation:
System #1: x=4
[tex]2x+y=10\\x-3y=-2[/tex]
To solve, start by isolating your first equation for y.
[tex]2x+y=10\\y=-2x+10[/tex]
Now, plug this value of y into your second equation.
[tex]x-3(-2x+10)=-2\\x+6x-30=-2\\7x=28\\x=4[/tex]
System #2: x=1
[tex]x+2y=5\\2x+y=4[/tex]
Isolate your second equation for y.
[tex]2x+y=4\\y=-2x+4[/tex]
Plug this value of y into your first equation.
[tex]x+2(-2x+4)=5\\x+(-4x)+8=5\\x-4x+8=5\\-3x=-3\\x=1[/tex]
System #3: x=6
[tex]5x+y=33\\x=18-4y[/tex]
Isolate your first equation for y.
[tex]5x+y=33\\y=-5x+33[/tex]
Plug this value of y into your second equation.
[tex]x=18-4(-5x+33)\\x=18+20x-132\\-19x=-114\\x=6[/tex]
System #4: all real numbers (not included in your diagram)
[tex]y=13-2x\\8x+4y=52[/tex]
Plug your value of y into your second equation.
[tex]8x+4(13-2x)=52\\8x+52-8x=52\\0=0[/tex]
all real numbers are solutions
System #5: x=2
[tex]x+3y=5\\6x-y=11[/tex]
Isolate your second equation for y.
[tex]6x-y=11\\-y=-6x+11\\y=6x-11[/tex]
Plug in your value of y to your first equation.
[tex]x+3(6x-11)=5\\x+18x-33=5\\19x=38\\x=2[/tex]
System #6: no solution (not included in your diagram)
[tex]2x+y=10\\-6x-3y=-2[/tex]
Isolate your first equation for y.
[tex]2x+y=10\\y=-2x+10[/tex]
Plug your value of y into your second equation.
[tex]-6x-3(-2x+10)=-2\\-6x+6x-30=-2\\-30=-2[/tex]
no solution
System #7: x=3
[tex]y=10+x\\2x+3y=45[/tex]
Plug your value of y into your second equation.
[tex]2x+3(10+x)=45\\2x+30+3x=45\\5x=15\\x=3[/tex]
