Solving systems with Sunstitution

[Young&&inlove]

Ohk here's the equation:
1/2x+3/4y=2
x+3y=7

Here's what I got but it isn't right.

x+3y=7
-3y -3y
x=7=3y

1/2(7-3y)+3/4y=2
3.5-1.5y_3/4y=2
3.5-1.5y+.75y=2
-.75y -.75y
3.5-.75y=2
-3.5 -3.5
.75y=-1.5
.75 .75
y=-2

x+3(-2)=7
x-6=7
+6 +6
x=13

1/2(13)+3/4(-2)=7
6.5-1.5=7
-1.5 -1.5
5=7??

I don't think thats right??
5 can't equal 7??
Where did I mess up??

Can you please get back to me tonight???

-Marissa.

 

[jonboy]

Ohk here's the equation:
1/2x+3/4y=2
x+3y=7

Here's what I got but it isn't right.

x+3y=7
-3y -3y
x=7=3y

1/2(7-3y)+3/4y=2
3.5-1.5y_3/4y=2
3.5-1.5y+.75y=2
-.75y -.75y <-You need to subtract the -.75y from the right side of the equal sign
3.5-.75y=2
-3.5 -3.5
.75y=-1.5
.75 .75
y=-2

x+3(-2)=7
x-6=7
+6 +6
x=13

1/2(13)+3/4(-2)=7
6.5-1.5=7
-1.5 -1.5
5=7??
I don't think thats right??
5 can't equal 7??
Where did I mess up??

Can you please get back to me tonight???

-Marissa.

 

[Mrspi]

Ohk here's the equation:
1/2x+3/4y=2
x+3y=7



Can you please get back to me tonight???

-Marissa.

We could get rid of the fractions in the first equation if we multiply both sides by 4, the LCD for the fractions:

4(1/2)x + 4(3/4)y = 4(2)
2x + 3y = 8

Ok...solve the second equation for x, and you get
x = 7 - 3y

NOW substitute (7 - 3y) for x in
2x + 3y = 8
2(7 - 3y) + 3y = 8
14 - 6y + 3y = 8
14 - 3y = 8
14 - 3y - 14 = 8 - 14
-3y = -6
y = 2

And you know that
x = 7 - 3y
Substitute 2 for y, and find the value for x.

Check to see that your values for x and y make both of the ORIGINAL equations true.

I hope this helps you.