Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 years ago

# how do you substitution method in both these equation 2x+3y=13.50 and 4x+2y=15.00?

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2x+3y=13.50 so (4x = 27-6y)

4x+2y=15.00

27-6y+2y=15

-4y = -12

y = 3

x = 9/4

• okie try to solve for either x or y first ....

Step one: (2x+3y=13.50)

(4x+2y=15.00)

now you want to find a number to multiply by either of those equations to cancel out x like in your case you can multiply the first equation by a negative 2

-2(2x+3y=13.50) sooo you gett ====> -4x-6y=27

so now put equations in such way to add them to make x =o

( -4x-6y=27)

( 4x+2y=15.00)

_________________

0 -4y=42

now to get y by itself divide both sides by -4

which will give you Y= 10.5

now pick either one the equations and plug in 10.5 for Y and you will get your answer......so for example lets pick the first equation

2x+3y=13.5

2x+3(10.5)=13.5 =====> 2x+31.5=13.5

now subtract 31.5 from both sides to get 2x by itselffff

2x+31.5=13.5

-31.5 -31.5

____________________

2x= -18

now to get x by itself divide both sides by 2

x=-9

to check that the answers are correct plug it both y and x in the same equation and your answer on the left hand side should equal the right hand side okie good luckkkkkkk

final answer ==== x= -9, y=10.5

• substitution means you solve for x (or y) in one equation and then plug it into the other. Now, the other equation only has one variable and can be solved. So start out by subtracting 3y so 2x=13.5-3y, divide by 2, etc. You'll now have x= some expression with y and plug that into the other equation for y.

• Anonymous
9 years ago

2 times first equation gives 4x + 6y =27, or 4x = 27-6y

Substituting, 27-6y +2y = 15

which gives y=3 and x= 9/4

• Dear Mia,

Here are the step by step you need to do...

2x+3y=13.5_4x+2y=15

Since 3y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 3y from both sides.

2x=-3y+13.5_4x+2y=15

Divide each term in the equation by 2.

(2x)/(2)=-(3y)/(2)+(13.5)/(2)_4x+2y=15

Simplify the left-hand side of the equation by canceling the common terms.

x=-(3y)/(2)+(13.5)/(2)_4x+2y=15

Combine the numerators of all expressions that have common denominators.

x=(-3y+13.5)/(2)_4x+2y=15

Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is ((-3y+13.5))/(2).

x=(-3y+13.5)/(2)_4((-3y+13.5)/(2))+2y=15

Remove the parentheses around the expression -3y+13.5.

x=(-3y+13.5)/(2)_4((-3y+13.5)/(2))+2y=15

Divide each term in the numerator by the denominator.

x=-(3y)/(2)+(13.5)/(2)_4((-3y+13.5)/(2))+2y=15

Divide 13.5 by 2 to get 6.75.

x=-(3y)/(2)+6.75_4((-3y+13.5)/(2))+2y=15

Remove the parentheses around the expression -3y+13.5.

x=-(3y)/(2)+6.75_4((-3y+13.5)/(2))+2y=15

Divide each term in the numerator by the denominator.

x=-(3y)/(2)+6.75_4(-(3y)/(2)+(13.5)/(2))+2y=15

Divide 13.5 by 2 to get 6.75.

x=-(3y)/(2)+6.75_4(-(3y)/(2)+6.75)+2y=15

Multiply 4 by each term inside the parentheses.

x=-(3y)/(2)+6.75_(-6y+27)+2y=15

Since -6y and 2y are like terms, subtract 2y from -6y to get -4y.

x=-(3y)/(2)+6.75_-4y+27=15

Since 27 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 27 from both sides.

x=-(3y)/(2)+6.75_-4y=-27+15

Add 15 to -27 to get -12.

x=-(3y)/(2)+6.75_-4y=-12

Divide each term in the equation by -4.

x=-(3y)/(2)+6.75_-(4y)/(-4)=-(12)/(-4)

Simplify the left-hand side of the equation by canceling the common terms.

x=-(3y)/(2)+6.75_y=-(12)/(-4)

Simplify the right-hand side of the equation by simplifying each term.

x=-(3y)/(2)+6.75_y=3

Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 3.

x=-(3(3))/(2)+6.75_y=3

Multiply -3 by 3 in the numerator.

x=(-3*3)/(2)+6.75_y=3

Multiply -3 by 3 to get -9.

x=(-9)/(2)+6.75_y=3

Move the minus sign from the numerator to the front of the expression.

x=-(9)/(2)+6.75_y=3

To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 2. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.

x=6.75*(2)/(2)-(9)/(2)_y=3

Complete the multiplication to produce a denominator of 2 in each expression.

x=(13.5)/(2)-(9)/(2)_y=3

Combine the numerators of all fractions that have common denominators.

x=(13.5-9)/(2)_y=3

Subtract 9 from 13.5 to get 4.5.

x=(4.5)/(2)_y=3

Divide 4.5 by 2 to get 2.25.

x=2.25_y=3

This is the solution to the system of equations.

x=2.25_y=3

Source(s): Precalculus Solved!