How to solve Linear Equations- Substitution?

Question

I am so confused right now! I need help. I'm frustrated and ready to scream. I'm having to teach myself the end of Algebra I.

I have no idea how to do this type of equation.

Here is an example:

Find the common solution for the equation:
2x+y=4
2x+3y=0

I love math, but this competely lost me.

Thanks in advance!!

Answer 1

solve equation 1 for (y)

y = 4-2x

sub into equation 2 and solve for (x)

2x + 3*(4-2x) = 0

2x + 12 - 6x = 0

-4x = -12

x = 3

sub back into equation 1

2*3 + y = 4

y = -2

check with equation 2

2*3 + 3*-2 = 0

Answer 2

The easiest variable to isolate is y in the first equation. Write the first equation as

y = -2x +4

Substitute the expression -2x + 4 in place of the the variable y of the second equation.

2x + 3(-2x + 4) = 0
2x - 6x + 12 = 0
-4x + 12 = 0
-4x = -12
x = 3

To find the valu of the variable y, we can substitute x = 3 into either of the original equations and solve for x. If we choose the first equation, then

2(3 ) + y = 4
6 + y = 4
y = -2

The solution of the system is (x, y) = (3, -2).

Answer 3

Write between the equations to have in basic terms one variable on between the perimeters: -2x + y = 7 y = 7 + 2x substitute (7 + 2x) for y in the different equation: 5x - 2(7 + 2x) = -sixteen sparkling up for x: 5x - 2(7 + 2x) = -sixteen 5x - 14 - 4x = -sixteen x = -2 substitute -2 for x in the two of the equations to get y: -2(x) + y = 7 -2(-2) + y = 7 4 + y = 7 y = 3

Answer 4

for web support look under "simultaneous equations"
e.g. http://www.mathsrevision.net/gcse/pages.php?page=3

for your problem subtract the second equation from the first to get rid of the "2x" terms
y-3y = 4 - 0 or -2y = 4 or y=-2

Substitute back in one of the equation
2x + (-2) =4 so 2x = 6 and x=3

Check your answers {x=3, y=-2} in the other equation
2(3) * 3(-2) = 0
6 - 6 = 0
0=0 so the answer checks

Rules:
manipulate the equations so you can eliminate one of the variables by subtracting one equation from the other.
ex. 5x + y =12
2x +3y = 3
to eliminate the x term, multiply the first equation by 2 and the second by 5 to get
10x + 2y = 24 and
10x +15y = 15

next, Solve for the remaining variable
substitute that solution back into one of the equations and solve for the other variable

Check your answers in the other equation

Answer 5

solve the first equation for y
y=4-2x
substitute this value of y into second equation
2x +3(4-2x) =0
2x +12 -6x =0
12=4x
x=3
now substitute the value of x back into the first equation
2(3) +y=4
y =4-6
y=-2

the solution is x=3 and y = -2

Answer 6

2x+3y=0
2x+y=4

Let's solve these by subtracting the second equation from the first.

We have

2y = -4
y = -2

Now to solve for x we will substitute y = -2 back into one of the equations.

Let's use 2x+y=4
then 2x + (-2) = 4

2x = 6

x = 3 and y = -2

.

Answer 7

2x+y=4
2x+3y=0

2x+y-4=2x+3y
0-4=2y
y=-2

substitute -2 to either equations, u get x=3

Answer 8

x=3
y=-2