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2x+y=20 -5y=-6x+12 what is the solution of the system of equations

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Final answer:

To solve the system of equations, use the method of elimination. Multiply the second equation by 2 to make the coefficients match, then add the equations to eliminate the x term. Solve for y by substituting the value of x back into either of the original equations.

Step-by-step explanation:

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination. We can start by multiplying the second equation by 2 to make the coefficients of y equal:

2x + y = 20

-12x + 10y = 24

Now, we can add the two equations together:

(2x + y) + (-12x + 10y) = 20 + 24

-10x + 11y = 44

Simplifying further:

11y = 10x + 44

y = (10/11)x + 4

Now we can substitute this value of y into either of the original equations to find the value of x. Let's use the first equation:

2x + y = 20

2x + (10/11)x + 4 = 20

(22/11)x + (10/11)x = 16

(32/11)x = 16

x = 16 * (11/32)

x = 5.5

Substituting this value of x back into the equation for y:

y = (10/11) * 5.5 + 4

y = 5 + 4

y = 9

So the solution to the system of equations is x = 5.5 and y = 9.

User Marcel Hoyer
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