Question

Find the solution of the system of equations.
5x – 2y = -5
5x + 6y= 35

Answer 1

To solve the system of equations, use the elimination method or substitution. The solution is x = 1/3 and y = 50/9.

Step-by-step explanation:

To solve the system of equations, we can use the method of elimination or substitution. Let's use the elimination method in this case. We'll add the two equations to eliminate the x-variable:

5x - 2y = -5

5x + 6y = 35

When we add the equations, the x-terms cancel out:

5x + 5x - 2y + 6y = -5 + 35

10x + 4y = 30

Now, we can solve this new equation for y:

10x + 4y = 30

4y = 30 - 10x

y = (30 - 10x)/4

Next, we substitute this value of y into one of the original equations:

5x - 2((30 - 10x)/4) = -5

Multiplying through by 4 to eliminate the fraction:

20x - (30 - 10x) = -20

20x - 30 + 10x = -20

30x - 30 = -20

30x = 10

x = 10/30

x = 1/3

Finally, we substitute this value of x back into one of the original equations to find the value of y:

5(1/3) + 6y = 35

5/3 + 6y = 35

6y = 35 - 5/3

6y = 35/1 - 5/3

6y = 105/3 - 5/3

6y = 100/3

y = (100/3)/6

y = 100/18

y = 50/9

Therefore, the solution to the system of equations is x = 1/3 and y = 50/9.

Answer 2

(1,5)

Step-by-step explanation:

Find a way to cancel out a variable, right now the easiest option is x because you only need to make one of the two negative like such:

-(5x-2y=-5)

5x+6y=35

^this becomes

-5x+2y= 5

5x +6y=35

When you add up the terms, the x cancels out and you’re left with

8y = 40

Now you need to solve for y by getting the variable by itself (divide by 8)

y = 5

Now, in order to find x, you need to plug y into one of the original equations

I’m going to choose 5x-2y=-5 simply because it has smaller numbers

So once you plug y in the equation should look like this:

5x-2(5)=-5

Multiply -2*5 and your equation should now be

5x-10=-5

Now you need to isolate the variable, first add 10 to both sides

5x-10+10= -5+10

5x=5

Divide by 5 to officially solve for x

x=1

The answer should, therefore be (1,5)

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