Question 66298: 1. 2x=y-1
y=3x
2. x=-y
2x+y=-2
3. 2x+2y=4
x=10-3y
4. y=7-x
2x+3y=-1
Solve by substitution. Check your answers.
I am new to Algebra 1 having trouble solving these problems.
Can you help!!!! Thanks
ISBN: 0-03-070039-6 pg 756 1-4 plus #6 ch 7.2
Found 2 solutions by checkley71, funmath:
Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website! SINCE Y=3X THEN WE SUBSTITUTE (3X) FOR Y IN THE OTHER EQUATION THUS
2X=3X-1
2X-3X=-1
-X=-1
X=1 SOLUTION.
NOW SUBSTITUTE 1 FOR X IN EITHER EQUATION & SOLVE FOR Y.
Y=3*1
Y=3 SOLUTION
---------------------------------------------------
X=-Y NOW SUBSTITUTE (-Y) FOR X IN THE OTHER EQUATION & SOLVE.
2(-Y)+Y=-2
-2Y+Y=-2
-Y=-2
Y=2 SOLUTION
X=-(-2)
X=2 SOLUTION
--------------------------------------------------
X=10-3Y SUBSTITUTE (10-3Y) FOR X IN THE OTHER EQUATION.
2(10-3Y)+2Y=4
20-6Y+2Y=4
-2Y=4-20
-2Y=-16
Y=-16/-2
X=8 SOLUTION
8=10-3Y
8-10=-3Y
-3Y=--2
Y=-2/-3
Y=2/3 SOLUTION
------------------------------------------------------------
Y=7-X
2X+3(7-X)=-1
2X+21-3X=-1
-X=-1-21
-X=-22
X=22 SOLUTION
Y=7-22
Y=-15 SOLUTION
---------------------------------
Answer by funmath(2933) (Show Source):
You can put this solution on YOUR website! 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
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