Question Solve the system of linear equations: $-2x + y = -2$ and $2x - y + 2 = 0$ .

Studdy Solution

STEP 1

Assumptions
1. We have a system of two linear equations.
2. The system is in the form of $ax + by = c$ .
3. The system can be solved using methods such as substitution, elimination, or graphing. We will use the elimination method.
The system of equations is: $\begin{aligned} -2 x+y & =-2 \\ 2 x-y+2 & =0 \end{aligned}$

STEP 2

In the elimination method, we add or subtract the equations in order to eliminate one of the variables. In this case, we can add the two equations to eliminate $y$ .
$(-2x + y) + (2x - y + 2) = -2 + 0$

STEP 3

Simplify the left-hand side of the equation by adding like terms.
$0x + 2 = 0$

STEP 4

Simplify the right-hand side of the equation.
$0x + 2 = -2$

STEP 5

Solve for $x$ .
Since $0x$ is $0$ , the equation simplifies to $2 = -2$ . This is a contradiction, meaning there is no solution for $x$ .

STEP 6

Since there is no solution for $x$ , there is no need to substitute $x$ into either of the original equations to solve for $y$ .
Therefore, the system of equations has no solution.

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Question Solve the system of linear equations: $-2x + y = -2$ and $2x - y + 2 = 0$ .

Studdy Solution

STEP 1

STEP 2

In the elimination method, we add or subtract the equations in order to eliminate one of the variables. In this case, we can add the two equations to eliminate $y$ .
$(-2x + y) + (2x - y + 2) = -2 + 0$

STEP 3

Simplify the left-hand side of the equation by adding like terms.
$0x + 2 = 0$

STEP 4

Simplify the right-hand side of the equation.
$0x + 2 = -2$

STEP 5

Solve for $x$ .
Since $0x$ is $0$ , the equation simplifies to $2 = -2$ . This is a contradiction, meaning there is no solution for $x$ .

STEP 6

Since there is no solution for $x$ , there is no need to substitute $x$ into either of the original equations to solve for $y$ .
Therefore, the system of equations has no solution.

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Question Solve the system of linear equations: −2x+y=−2-2x + y = -2−2x+y=−2 and 2x−y+2=02x - y + 2 = 02x−y+2=0.

Studdy Solution

STEP 1

STEP 2

In the elimination method, we add or subtract the equations in order to eliminate one of the variables. In this case, we can add the two equations to eliminate yyy.(−2x+y)+(2x−y+2)=−2+0(-2x + y) + (2x - y + 2) = -2 + 0(−2x+y)+(2x−y+2)=−2+0

STEP 3

Simplify the left-hand side of the equation by adding like terms.0x+2=00x + 2 = 00x+2=0

STEP 4

Simplify the right-hand side of the equation.0x+2=−20x + 2 = -20x+2=−2

STEP 5

Solve for xxx.Since 0x0x0x is 000, the equation simplifies to 2=−22 = -22=−2. This is a contradiction, meaning there is no solution for xxx.

STEP 6

Since there is no solution for xxx, there is no need to substitute xxx into either of the original equations to solve for yyy. Therefore, the system of equations has no solution.

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Question Solve the system of linear equations: $-2x + y = -2$ and $2x - y + 2 = 0$ .

In the elimination method, we add or subtract the equations in order to eliminate one of the variables. In this case, we can add the two equations to eliminate $y$ .
$(-2x + y) + (2x - y + 2) = -2 + 0$

Simplify the left-hand side of the equation by adding like terms.
$0x + 2 = 0$

Simplify the right-hand side of the equation.
$0x + 2 = -2$

Solve for $x$ .
Since $0x$ is $0$ , the equation simplifies to $2 = -2$ . This is a contradiction, meaning there is no solution for $x$ .

Since there is no solution for $x$ , there is no need to substitute $x$ into either of the original equations to solve for $y$ .
Therefore, the system of equations has no solution.