# Simultaneous equation substitution method x+y=3 and 5x_5y=1

## assume you mean

x+y=3 and 5x-5y=1
so you can say y = 3 - x and substitute that in the second equation
5 x - 5 (3-x) = 1
5 x - 15 + 5 x = 1
10 x = 16
x = 1.6
then y = 3 - 1.6 = 1.4
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check
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5 x = 8
5 y = 7
sure enough 8 - 7 = 1

## To solve the simultaneous equations x + y = 3 and 5x - 5y = 1 using the substitution method, we can isolate one variable in one equation and substitute it into the other equation. Here's how to do it step-by-step:

Step 1: Solve one equation for one variable.
In the first equation, x + y = 3, isolate x:
x = 3 - y

Step 2: Substitute the expression for x into the other equation.
In the second equation, replace x with (3 - y):
5(3 - y) - 5y = 1

Step 3: Solve the equation.
Distribute the 5 on the left side:
15 - 5y - 5y = 1

Combine like terms:
15 - 10y = 1

Step 4: Solve for y.
Subtract 15 from both sides:
-10y = 1 - 15

Simplify:
-10y = -14

Divide both sides by -10:
y = -14 / -10
y = 7/5 or 1.4

Step 5: Substitute the value of y back into the first equation to solve for x.
Using x + y = 3:
x + (7/5) = 3

Subtract (7/5) from both sides:
x = 3 - (7/5)

Simplify:
x = 15/5 - 7/5
x = 8/5 or 1.6

So, the solution to the simultaneous equations x + y = 3 and 5x - 5y = 1 is x = 1.6 and y = 1.4.

## To solve the simultaneous equations using the substitution method, we can solve one equation for one variable and substitute it into the other equation. Let's start with the first equation:

Equation 1: x + y = 3

We can solve this equation for x by subtracting y from both sides:

x = 3 - y

Now, let's substitute this expression for x in the second equation:

Equation 2: 5x - 5y = 1

Substituting x = 3 - y into Equation 2, we have:

5(3 - y) - 5y = 1

Simplifying, we distribute the 5:

15 - 5y - 5y = 1

Combine like terms:

-10y + 15 = 1

Next, we isolate the term with y by subtracting 15 from both sides:

-10y = 1 - 15

-10y = -14

Divide both sides by -10 to solve for y:

y = -14 / -10

Simplifying further:

y = 7 / 5

Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:

x + (7 / 5) = 3

Subtract (7 / 5) from both sides:

x = 3 - (7 / 5)

To simplify, multiply 3 by 5/5 to get a common denominator:

x = (15 / 5) - (7 / 5)

x = (15 - 7) / 5

x = 8 / 5

Therefore, the solution to the simultaneous equations x + y = 3 and 5x - 5y = 1 is x = 8/5 and y = 7/5.