how to solve this using substitution method

Question

x+2y=4

3x-4y=-3

Answer 1

How to solve using substitution:

 

1. First you decide which equation you want to solve for either the x or the y.  It does not matter which one you do as long as you solve it correctly. However, if there is any variable without a coefficient, that is the easiest one to choose since you do not have to deal with fractions right away.

 

Solve equation 1 for x by subtracting 2y from both sides

equation 1:  x+2y=4
equation 2:  3x-4y=-3

 

Now you have x= 4-2y and 3x-4y=-3

 

2. Substitute 4-2y into the second equation for the x and solve for y.

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

 

12-6y-4y=-3               Distribute

12-10y=-3                  Add like terms

-10y=-15                    Add negative 12 to both sides to move the 12 over and get the y term by itself

y=15/10                     Divide both sides by -10. A negative divided by a negative is a positive

y=3/2                         Reduce

 

3. Now substitute 3/2 into the equation solved for x to find out what x equals.

x=4-2(3/2)                 The 2s cancel

x=4-3                         Subtract

x=1

 

Answer:  x=1 and y=3/2  (1, 3/2)

 

4. You can check answer by plugging these values into both equations so see that they work correctly.

 

x+2y=4

1+2(3/2)=1+3=4=4

3x-4y=-3

3(1)-4(3/2)=3-6=-3=-3

Answer 2

Hi Cristina,

 

x+2y=4

 

x=4-2y     equation 1

 

3x-4y=-3    equation 2

 

substitute the value of x from equation 1 in equation 2

 

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

 

12-6y-4y=-3

 

12-10y=-3

 

12-12-10y=-3-12

 

-10y=-15

 

-10y/-10=-15/-10

 

y=3/2

 

substitute the value of y=3/2 in equation 1

 

x=4-2y

 

x=4-2(3/2)

 

x=4-3=1

 

The solution is x=1 and y=3/2

 

CHECK:

 

x+2y=4

 

1+2(3/2)=1+3=4=4

 

3x-4y=-3

 

3(1)-4(3/2)=3-6=-3=-3