Question

What is the first step to solve the following system of equations using substitution?

X-y=-1
2x-y=3
A.) Solve the first equation for x.
B.) Divide the second equation by 2.
C.) Multiply the first equation by 2.
D.) Add the two equations together.

Answer 1

The first step to solve the system of equations using substitution is to solve the first equation for x. Then, substitute this expression into the second equation to find the value of y.

Step-by-step explanation:

The first step to solve the system of equations using substitution is to solve the first equation for x.

To do this, we will isolate x by adding y to both sides of the equation:

X - y = -1
X = y - 1

Now that we have solved the first equation for x, we can substitute this expression into the second equation to find the value of y.

Substituting y - 1 for x in the second equation:

2(y - 1) - y = 3
2y - 2 - y = 3
y - 2 = 3
y = 5

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

X - 5 = -1
X = 4

So the solution to the system of equations is x = 4 and y = 5.

Answer 2

Step 1: Solve one of the equations for one of the variables. Let's solve the first equation for x

Thus, option A) is true.

The solution to the system of equations be:

`x = 4, y = 5`

Step-by-step explanation:

It is important to remember that when we solve the system of equations, the first step we need to do is to solve one of the equations for one of the variables.

Given the system of equations

`x - y = -1`

`2x - y = 3`

Step 1: Solve one of the equations for one of the variables. Let's solve the first equation for x

`x-y=-1`

Add y to both sides

`x-y+y=-1+y`

`x=-1+y`

Thus, option A) is true.

NOW LET US SOLVE THE REMAINING PORTION

`\mathrm{Subsititute\:}x=-1+y` to solve for y

`\begin{bmatrix}2\left(-1+y\right)-y=3\end{bmatrix}`

`-2+y=3`

`y=5`

For x = -1 + y

substitute y = 5

`x=-1+5`

`x=4`

Thus, the solution to the system of equations be:

`x = 4, y = 5`