Question

Use the substitution method to solve the system { −x+y=1

4x−3y=−5
​.
Your answer is x=........... y=....................

Answer 1

To solve the system of equations using the substitution method, solve one equation for one variable and substitute it into the other equation. The solution to the given system of equations is x = -2 and y = 3.

Step-by-step explanation:

To solve the system of equations using the substitution method, we start by solving one equation for one variable and substituting it into the other equation.

In this case, we can solve the first equation for x:

-x + y = 1
y = x + 1

Now, we substitute this expression for y in the second equation:

4x - 3(x + 1) = -5

Simplifying, we have:

x = -2

Now, we substitute this value of x back into the first equation to solve for y:

-(-2) + y = 1

y = 3

So, the solution to the system of equations is x = -2 and y = 3.

Answer 2

The solution to the system of equations −x + y = 1 and 4x − 3y = −5 using the substitution method is x = -2 and y = -1.

Step-by-step explanation:

To solve the system of equations −x + y = 1 and 4x − 3y = −5 using the substitution method, we first solve one of the equations for one variable and then substitute that expression into the other equation. Let's solve the first equation for x:

x = y - 1

Now substitute this expression for x into the second equation:

4(y - 1) - 3y = -5

4y - 4 - 3y = -5

y - 4 = -5

y = -1

With the value of y, we can now determine x:

x = y - 1

x = -1 - 1

x = -2

Therefore, the solution to the system of equations is x = -2 and y = -1.