Question

X plus Y equals 5X plus Y equals -3 solve the following system of equations using substitution

Answer 1

To solve the system of equations using substitution, we can solve one equation for one variable and substitute it into the other equation.

Let's solve the first equation for X:

X + Y = 5

Subtracting Y from both sides gives us:

X = 5 - Y

Now, substitute this expression for X into the second equation:

5X + Y = -3

Substituting 5 - Y for X gives us:

5(5 - Y) + Y = -3

Distribute the 5:

25 - 5Y + Y = -3

Combine like terms:

-4Y + 25 = -3

Subtract 25 from both sides:

-4Y = -28

Divide by -4:

Y = 7

Now that we have the value for Y, substitute it back into one of the original equations to solve for X. We'll use the first equation:

X + Y = 5
X + 7 = 5

Subtract 7 from both sides:

X = -2

Therefore, the solution to the system of equations is X = -2 and Y = 7.