# Solve the system of equations:3x-y= 5 5x-2y = 3

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### 4 Answers

We have to solve the system of equations:

3x - y = 5 ...(1)

5x - 2y = 3 ...(2)

From (1)

3x - y = 5

=> y = 3x - 5

substitute in (2)

=> 5x - 2(3x - 5) = 3

=> 5x - 6x + 10 = 3

=> -x = -7

=> x = 7

y = 3x - 5 = 16

**The solution of the system of equations is x = 7 and y = 16.**

Given the system of equations:

3x - y= 5............(1)

5x -2y = 3...........(2)

We will solve the system using the substitution method.

We will rewrite equation (1).

==> y= 3x - 5.

Now we will substitute into (2).

==> 5x - 2(3x-5) = 3

==> 5x - 6x + 10 = 3

==> -x = -7==> x= 7

==> y= 3x-5 = 3*7 -5 = 21-5 = 16

**Then the solution is the pair ( 7, 16) **

3x - y = 5

5x - 2y = 3

First, multiply everything in the first equation by 2

By multiplying, your equation should look like

**6x - 2y = 10**

**5x - 2y = 3 **subtract the -2y with -2y ( which means subtract 6x with 5x and 10 with 3)

By subtracting, your equation should look like

**x = 7 **which is your answer for " x "

Now, plug 7 into one of the equation

**3 ( 7 ) - y = 5 **now multiply 7 with 3

By multiplying, your equation should look like

**21 - y = 5 **now subtract both sides by 21

By subtracting your equation should look like

**-y = -16 **now divide both sides by -1

By dividing, your equation should look like

**y = 16**

So your answer is **x = 7 ; y = 16**

3x-y=5

3x-y-3x=5-3x

-y=5-3x

-y/-1=5/-1-3x/-1

y=-5x+3x

5x-2(-5+3x)=3

5x+10-6x=3

-1x+10=3

-1+10-10=3-10

-1x/-1=7/-1

**x=7**

5(7)-2y=3

35-2y=3

35-2y-35=3-35

-2y/-2=-32/-2

**y=16**