Question

Solve the system of equations by substitution:

a) ( x = -1, , y = 2 )

b) ( x = 2, , y = -3 )

c) ( x = -3, , y = 10 )

d) ( x = 0, , y = 1 )

Answer 1

a) (x = -1, y = 2)

Step-by-step explanation:

To solve the system of equations by substitution, we substitute the expression for one variable from one equation into the other. Consider the system:

`\[ \begin{cases} 2x - y = -3 \\ 3x + 2y = 1 \end{cases} \]`

Solving the first equation for (y), we get (y = 2x + 3). Substituting this into the second equation:

[ 3x + 2(2x + 3) = 1 ]

Now, solve for (x):

[ 3x + 4x + 6 = 1 ]

Combine like terms:

[ 7x + 6 = 1 ]

Subtract 6 from both sides:

[ 7x = -5 ]

Divide by 7:

\[ x = -\frac{5}{7} \]

Now, substitute \(x\) back into the first equation to find \(y):

`\[ 2\left(-(5)/(7)\right) - y = -3 \]`

Solving for (y):

`\[ -(10)/(7) - y = -3 \]`

Subtract
`\(-(10)/(7)\)` from both sides:

`\[ -y = -(11)/(7) \]`

Divide by -1:

`\[ y = (11)/(7) \]`

So, the solution is
`\(a) (x = -1, y = 2)\)`. The other options do not match the correct solution.