What is the solution to this system of equa
4x + 5y = 7
3x - 2y = -12

Step-by-step explanation:

Given:

4x + 5y = 7

3x - 2y = -12

Solve for:

x and y

Solution:

Step 1: Find the good approach

There are plenty of ways to solve system of linear equations. For a problem requiring solving only 2 variables, one of the good methods is trying to eliminate all components containing 1 variable, then solve for remaining variable only. Afterwards, substitute the variable found, back into one of original equations to work out the eliminated variable.

Step 2: Perform the calculation

Transform the original system into new one which is easier for eliminating:

4x + 5y = 7

3x - 2y = -12

<=>

3*(4x + 5y) = 3*7 (multiply both sides of 1st equation by 3)

4*(3x - 2y) = 4*(-12) (multiply both sides of 2nd equation by 4)

As you might see, we intentionally try to create the components containing x, that share the same coefficient ( 3 x 4 = 4 x 3 = 12), this would help the next eliminating step.

<=>

12x + 15y = 21

12x - 8y = -48

Now, we see that if we subtract 2nd equation from 1st equation, we will completely eliminate components containing x.

<=>

(12x - 12x) + (15y - (-8y) = 21 - (-48)

Then, we do the simplification:

<=>

23y = 69

We finally divide both sides of equation by 23, to work out y.

<=> (23/23)y = 69/23

<=> y = 3

Now we substitute y back into 1st original equation, we have:

4x + 5y = 7 or 4x + 5*3 = 7

<=> 4x + 15 = 7

We move all numbers to the right side, except the components containing x (notice the change of sign of number from + to -)

<=> 4x = 7 - 15

<=> 4x = -8

We finally divide both sides of equation by 4, to work out x.

<=> (4/4)x = -8/4

<=> x = -2

Now, we conclude the solution of this system of linear equation is:

(x, y) = (-2, 3)

Hope this helps!

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step-by-step explanation: