3/4x+1/2y=15

1/2x+4/6y=13

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

3/4 X + 1/2 y = 15

1/2 X + 4/6 y = 13

Multiply the first equation by 4:

- (3X + 2Y = 60)

3X + 4y = 78 ( 2nd equation by 6)

Now by method of elimination we subract first equation from the 2nd.

2Y = 18 Y = 9

Substitue Y = 9

3X +18 = 60

3X = 42 X = 14

Hi Ahmad;

3/4x+1/2y=15

1/2x+4/6y=13

1/2x+4/6y=13

I am assuming this is...

(3/4)x+(1/2)y=15

(1/2)x+(4/6)y=13

Let's begin with the first equation...

(3/4)x+(1/2)y=15

Fractions are so confusing. Let's note that the denominators (also known as divisors) are 4 and 2. Let's multiply everything by 4...

4[(3/4)x+(1/2)y]=4(15)

3x+2y=60

Let's proceed with the second equation...

(1/2)x+(4/6)y=13

Let's multiply both sides by 6...

6[(1/2)x+(4/6)y]=6(13)

3x+4y=78

3x+4y=78

3x+2y=60

Let's subtract the first equation from the second...

0+2y=18

2y=18

Let's divide both sides by 2...

(2y)/2=18/2

y=9

Original equations...

(3/4)x+(1/2)y=15

Let's plug-in 9...

(3/4)x+(1/2)(9)=15

(3/4)x+4.5=15

Let's subtract 4.5 from both sides...

(3/4)x+4.5-4.5=15-4.5

(3/4)x=10.5

Let's multiply both sides by (4/3)...

(4/3)(3/4)x=10.5(4/3)

x=42/3=14

(1/2)x+(4/6)y=13

Let's plug in y=9 and x=14 to verify...

(1/2)(14)+(4/6)(9)=13

7+(36/6)=13

7+6=13

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