SOLUTION: Solve the system by the elimination method. What is the solution of the system? 5x + 3y = -7 7x

SOLUTION: Solve the system by the elimination method. What is the solution of the system? 5x + 3y = -7 7x - 2y = 19 The solution is ?

Question 430302: Solve the system by the elimination method. What is the solution of the system?
5x + 3y = -7
7x - 2y = 19
The solution is ?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
with the elimination method, you multiply one or both of the equations by factors that allow you to eliminate one of the unknown variables after you add or subtract one equation from the other.

your equations are:

5x + 3y = -7
7x - 2y = 19

multiply the first equation by 2 and multiply the second equation by 3 to get:

10x + 6y = -14
21x - 6y = 57

add the 2 equations together to get:

31x = 43

divide both sides of this equation by 31 to get:

x = 43/31

substitute for x in the first original equation to get:

5x + 3y = -7 becomes:

5*(43/31) + 3y = -7

subtract 5*(43/31) from both sides of this equation to get:

3y = -7 - 5*(43/31)

multiply both sides of this equation by 31 to get:

3*31*y = -7*31 - 5*43

simplify to get:

93*y = -217 - 215

simplify further to get:

93*y = -432

divide both sides of this equation by 93 to get:

y = -432/93

this can be reduced to y = -144/31

your values for x and y are:

x = 43/31
y = -144/31

plug these values into the original equations to see if the equations are true.

the 2 original equations are:

5x + 3y = -7
7x - 2y = 19

replacing x with 43/31 and y with -144/31, we get:

5*(43/31) + 3*(-144/31) = -7
7*(43/31) - 2*(-144/31) = 19

I used my calculator to confirm that both these equations are true.

this means that the values for x and y are good.

they are:

x = 43/31
y = -144/31

a graph of these 2 equations is shown below:

x = 43/31 is equivalent to x = 1.39

y = -144/31 is equivalent to y = -4.65

you can see from the graph that the intersection of the 2 lines is somewhere around (x,y) = (1.39,-4.65).

in order to graph these equations, you had to solve for y.

the 2 equations that were graphed were:

y = (-5x-7)/3 and y = (-7x+19)/(-2)

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