Answer :
y=5x-7 -3x-2y=-12 (2,3)
y=4x+3 y=-x-2 (-1,-1)
12x+8y=140 5 adults 10 children
12(5)+8(10)=140
60+80=140
y=4x+3 y=-x-2 (-1,-1)
12x+8y=140 5 adults 10 children
12(5)+8(10)=140
60+80=140
Answer: 1) A. (2, 3)
2) B. (-1, -1)
3) 10 children
Step-by-step explanation:
1) [tex]\left \{ {{y=5x-7} \atop {-3x-2y=-12}} \right.[/tex]
Since the y is already isolated in the first equation, to solve the system you simply substitute that expression into the second equation and then solve, finding the value of x:
[tex]-3x-2(5x-7)=-12\\-3x-10x+14=-12\\-13x=-12-14\\-13x=-26\\x=\frac{26}{13}=2[/tex]
And then you substitute that value into the first equation and solve to find the value of y:
[tex]y=5(2)-7\\y=10-7\\y=3[/tex]
So, the solution of the system is (2, 3).
2) [tex]\left \{ {{y=4x+3} \atop {y=-x-2}} \right.[/tex]
Since the y is already isolated in both equations, to solve the system you simply equalize the first and the second expression and then solve, finding the value of x:
[tex]4x+3=-x-2\\4x+x=-2-3\\5x=-5\\x=-1[/tex]
And then you substitute that value into the first or the second equation (whichever you like) and solve to find the value of y:
[tex]y=-(-1)-2\\y=1-2\\y=-1[/tex]
So, the solution of the system is (-1, -1).
3) [tex]\left \{ {{x+y=15} \atop {12x+8y=140}} \right.[/tex]
To solve the system, the easiest way is to isolate the y in the first equation and then substitute the expression obtained into the second equation, finding the value of x.
From the first equation: [tex]y=15-x[/tex]
Substituting:
[tex]12x+8(15-x)=140\\12x+120-8x=140\\4x=140-120\\4x=20\\x=5[/tex]
And then you substitute that value into the first equation and find the value of y:
[tex]y=15-5\\y=10[/tex]
So, there were 10 children in the group.
