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# 4x + 5y = 12, 3x + 4y = 10

Systems?

### 2 Answers by Expert Tutors

Kathryn M. | Certified Math and Science Teacher, Available for EOC and FSA TutoringCertified Math and Science Teacher, Avai...
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Here is another way to solve this problem.

To solve it, what you want to do is isolate one of the x's or y's, plug what you get into one equation, solve for one variable, and then other (phew... that was a lot to write... let me just show you).

Our equations are:   4x + 5y = 12   and   3x + 4y = 10

WE GOT THIS!

1. Solve for a variable. We will use the 2nd equation and solve for "x."

3x + 4y = 10   ---->  3x = 10 - 4y  ----> x = (10/3) - (4y/3).

2. Look! Now we know what x is! Let's plug this into the first equation!!!

4x + 5y = 12  ----> 4(10/3) - (4y/3) = 12 ----> (40/3) - (4y/3) = 12

3. Isolate and solve for the "y" variable.

(-4y/3) = 12 - (40/3) ----> y = 4

4. LOOK! We know what "y" is. Plug this in to either equation to get "x!"

4x + 5y = 12    ----> 4(x) + 5(4) = 12   ----> 4x = -8   ----> x = -2

Ralph L. | Algebra I, II, Visual Basic, Beginning C++ tutorAlgebra I, II, Visual Basic, Beginning C...
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4x + 5y = 12

3x + 4y = 10

multiply top equation by -4 and bottom equation by 5:

-4 ( 4x + 5y) = 12 * -4

-16x - 20y = -48

5 (3x +4y) = 10 * 5

15x + 20y = 50

so, now the equations are:

-16x - 20y = -48

15x + 20y = 50

add the two equations to eliminate y:

-x = 2 or x = -2

plug in -2 for x to either original equations to get y:

4 * -2 + 5y = 12

-8 + 5y = 12

-8 - 12 = -5y

-20 = -5y

divide both sides of equation by -5 to get y:

-20/ -5 = -5y / -5

4 = y or y = 4

.

let's plug in these values to both original equations:

4 * -2 + 5 * 4 = -8 + 20 = 12      this checks out

3 * -2 + 4 * 4 = -6 + 16 = 10      this check out

so, x = -2, y = 4