Question

solve the system with elimination 5x+4y=6 and -2x-3y=-1

Answer 1

To solve the system using elimination, we want to eliminate one of the variables by manipulating the equations in such a way that when we add them, one of the variables will cancel out.

To do this, we will multiply the second equation by 4 so that the coefficients of y in both equations will be -12 and 12, respectively:

First equation: 5x + 4y = 6
Second equation (multiplied by 4): -8x - 12y = -4

Now, we can add the two equations:

(5x + 4y) + (-8x - 12y) = 6 + (-4)
-3x - 8y = 2

Simplifying, we have:

-3x - 8y = 2

Now, we have a new equation:

-3x - 8y = 2

Let's solve this equation for one variable (y):

-8y = 2 + 3x
y = (2 + 3x)/-8
Next, substitute this expression for y into one of the original equations. Let's use the first equation:

5x + 4((2 + 3x)/-8) = 6
Multiplying both sides by -8 to remove the fraction:

-40x - 32 - 12x = -48
-52x - 32 = -48
-52x = -48 + 32
-52x = -16
Solving for x:

x = -16/-52
x = 4/13

Now, substitute this value of x back into the equation we obtained for y:

y = (2 + 3(4/13))/-8
y = (2 + 12/13)/-8
y = (26/13 + 12/13)/-8
y = 38/13 / -8
y = 38/13 * -1/8
y = -38/104
y = -19/52

Therefore, the solution to the system of equations is x = 4/13 and y = -19/52.