Question 66298
1. 
E1) 2x=y-1           
E2)   y=3x
Let y=3x in E1 and solve for x:
2x=3x-1
2x-3x=3x-3x-1
-x=-1
-(-x)=-(-1)
x=1
Now let x=1 in E2 and solve for y:
y=3(1)
y=3
The answer (x,y)=(1,3)
To check your answer, let x=1 and y=3 in both equations and see if they balance:
E1) 2(1)=(3)-1 
2=2 We're right for the 1st equation.
E2) (3)=3(1)
3=3 We're right for both equations.
:
2.
E1) x=-y
E2)   2x+y=-2
Let x=-y in E2 and solve for y:
2(-y)+y=-2
-2y+y=-2
-y=-2
-(-y)=-(-2)
y=2
Now let y=2 in E1 and solve for x:
x=-(2)
x=-2
The answer (x,y)=(-2,2)
Check:
E1) (-2)=-(2)
-2=-2  So far so good.
E2)  2(-2)+(2)=-2
-4+2=-2
-2=-2  We're really good.
:
3. 
E1) 2x+2y=4
E2)   x=10-3y
Let x=10-3y in E1 and solve for y:
2(10-3y)+2y=4
20-6y+2y=4
20-4y=4
20-20-4y=4-20
-4y=-16
-4y/-4=-16/-4
y=4
Now let y=4 in E2 and solve for x:
x=10-3(4)
x=10-12
x=-2
The answer is (x,y)=(-2,4)
Check:
E1) 2(-2)+2(4)=4
-4+8=4
4=4  So far we're right.
E2) (-2)=10-3(4)
-2=10-12
-2=-2  We're completely right!!!
:
4. 
E1)  y=7-x
E2)   2x+3y=-1
Let y=7-x in E2 and solve for x:
2x+3(7-x)=-1
2x+21-3x=-1
-x+21=-1
-x+21-21=-1-21
-x=-22
-(-x)=-(-22)
x=22
Let x=22 in E1 and solve for y:
y=7-22
y=-15
The answer is (x,y)=(22,-15)
Check:
E1) (-15)=7-(22) 
-15=-15  We're on the right track.
E2) 2(22)+3(-15)=-1
44-45=-1
-1=-1  We're on a roll!!!
Happy Calculating!!!!                   
ISBN: 0-03-070039-6 pg 756 1-4 plus #6 ch 7.2