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Question
\left\{ \begin{array}{l}y=x+7\\x=2\end{array}\right.
Solve the system of equations
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Solve using the substitution method
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Solve using the elimination method
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Solve using the Gauss-Jordan method
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Solve using the Cramer's rule
More methods
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\left(x,y\right) = \left(2,9\right)
Evaluate
\left\{ \begin{array}{l}y=x+7\\x=2\end{array}\right.
\text{Substitute the given value of }x\text{ into the equation }y=x+7
y=2+7
Simplify
y=9
Calculate
\left\{ \begin{array}{l}x=2\\y=9\end{array}\right.
Check the solution
More Steps
Check the solution
\left\{ \begin{array}{l}9=2+7\\2=2\end{array}\right.
Simplify
\left\{ \begin{array}{l}9=9\\2=2\end{array}\right.
Evaluate
\textrm{true}
\left\{ \begin{array}{l}x=2\\y=9\end{array}\right.
Solution
\left(x,y\right) = \left(2,9\right)
\left(x,y\right) = \left(2,9\right)
Evaluate
\left\{ \begin{array}{l}y=x+7\\x=2\end{array}\right.
Rewrite the equation
\left\{ \begin{array}{l}-x+y=7\\x=2\end{array}\right.
\text{Substitute the given value of }x\text{ into the equation }-x+y=7
-2+y=7
Calculate
y=9
Calculate
\left\{ \begin{array}{l}x=2\\y=9\end{array}\right.
Check the solution
More Steps
Check the solution
\left\{ \begin{array}{l}9=2+7\\2=2\end{array}\right.
Simplify
\left\{ \begin{array}{l}9=9\\2=2\end{array}\right.
Evaluate
\textrm{true}
\left\{ \begin{array}{l}x=2\\y=9\end{array}\right.
Solution
\left(x,y\right) = \left(2,9\right)
\left(x,y\right) = \left(2,9\right)
Evaluate
\left\{ \begin{array}{l}y=x+7\\x=2\end{array}\right.
Rewrite the equation
\left\{ \begin{array}{l}-x+y=7\\x=2\end{array}\right.
Write the system of equations in matrix form
\left[\begin{array}{ll|l}{-1}&{1}&{7}\\{1}&{0}&{2}\end{array}\right]
\text{Multiply the row by }-1
More Steps
Evaluate
\left[\begin{array}{ll|l}{-\left(-1\right)}&{1\times \left(-1\right)}&{7\left(-1\right)}\\{1}&{0}&{2}\end{array}\right]
Evaluate
\left[\begin{array}{ll|l}{1}&{1\times \left(-1\right)}&{7\left(-1\right)}\\{1}&{0}&{2}\end{array}\right]
Evaluate
\left[\begin{array}{ll|l}{1}&{-1}&{7\left(-1\right)}\\{1}&{0}&{2}\end{array}\right]
Evaluate
\left[\begin{array}{ll|l}{1}&{-1}&{-7}\\{1}&{0}&{2}\end{array}\right]
\left[\begin{array}{ll|l}{1}&{-1}&{-7}\\{1}&{0}&{2}\end{array}\right]
\text{Multiply row }1\text{ by }-1\text{ and add it to row }2
More Steps
Evaluate
\left[\begin{array}{ll|l}{1}&{-1}&{-7}\\{1+1\times \left(-1\right)}&{0-\left(-1\right)}&{2-7\left(-1\right)}\end{array}\right]
Evaluate
\left[\begin{array}{ll|l}{1}&{-1}&{-7}\\{0}&{0-\left(-1\right)}&{2-7\left(-1\right)}\end{array}\right]
Evaluate
\left[\begin{array}{ll|l}{1}&{-1}&{-7}\\{0}&{1}&{2-7\left(-1\right)}\end{array}\right]
Evaluate
\left[\begin{array}{ll|l}{1}&{-1}&{-7}\\{0}&{1}&{9}\end{array}\right]
\left[\begin{array}{ll|l}{1}&{-1}&{-7}\\{0}&{1}&{9}\end{array}\right]
\text{Add the row }2\text{ to the row }1
More Steps
Evaluate
\left[\begin{array}{ll|l}{1}&{-1+1}&{-7+9}\\{0}&{1}&{9}\end{array}\right]
Evaluate
\left[\begin{array}{ll|l}{1}&{0}&{-7+9}\\{0}&{1}&{9}\end{array}\right]
Evaluate
\left[\begin{array}{ll|l}{1}&{0}&{2}\\{0}&{1}&{9}\end{array}\right]
\left[\begin{array}{ll|l}{1}&{0}&{2}\\{0}&{1}&{9}\end{array}\right]
Write the matrix as a system of equations
\left\{ \begin{array}{l}x=2\\y=9\end{array}\right.
Check the solution
More Steps
Check the solution
\left\{ \begin{array}{l}9=2+7\\2=2\end{array}\right.
Simplify
\left\{ \begin{array}{l}9=9\\2=2\end{array}\right.
Evaluate
\textrm{true}
\left\{ \begin{array}{l}x=2\\y=9\end{array}\right.
Solution
\left(x,y\right) = \left(2,9\right)
\left(x,y\right) = \left(2,9\right)
Evaluate
\left\{ \begin{array}{l}y=x+7\\x=2\end{array}\right.
Rewrite the equation
\left\{ \begin{array}{l}-x+y=7\\x=2\end{array}\right.
List all the needed determinants
\begin{align}&D=\left|\begin{array}{cc}{1}&{-1}\\{0}&{1}\end{array}\right|\\&D_{1}=\left|\begin{array}{cc}{7}&{-1}\\{2}&{1}\end{array}\right|\\&D_{2}=\left|\begin{array}{cc}{1}&{7}\\{0}&{2}\end{array}\right|\end{align}
Evaluate the determinant using cofactor expansion
More Steps
Evaluate the determinant
\left|\begin{array}{cc}{1}&{-1}\\{0}&{1}\end{array}\right|
\text{Evaluate the determinant using the formula }\left| \begin{array} { l l l } { a } & { b } \\ { c } & { d } \end{array} \right| = ad - bc
1\times 1-\left(-1\times 0\right)
Any expression multiplied by 1 remains the same
1-\left(-1\times 0\right)
Any expression multiplied by 0 equals 0
1-0
Removing 0 doesn't change the value,so remove it from the expression
1
\begin{align}&D=1\\&D_{1}=\left|\begin{array}{cc}{7}&{-1}\\{2}&{1}\end{array}\right|\\&D_{2}=\left|\begin{array}{cc}{1}&{7}\\{0}&{2}\end{array}\right|\end{align}
Evaluate the determinant using cofactor expansion
More Steps
Evaluate the determinant
\left|\begin{array}{cc}{7}&{-1}\\{2}&{1}\end{array}\right|
\text{Evaluate the determinant using the formula }\left| \begin{array} { l l l } { a } & { b } \\ { c } & { d } \end{array} \right| = ad - bc
7\times 1-\left(-2\right)
Any expression multiplied by 1 remains the same
7-\left(-2\right)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
7+2
Add the numbers
9
\begin{align}&D=1\\&D_{1}=9\\&D_{2}=\left|\begin{array}{cc}{1}&{7}\\{0}&{2}\end{array}\right|\end{align}
Evaluate the determinant using cofactor expansion
More Steps
Evaluate the determinant
\left|\begin{array}{cc}{1}&{7}\\{0}&{2}\end{array}\right|
\text{Evaluate the determinant using the formula }\left| \begin{array} { l l l } { a } & { b } \\ { c } & { d } \end{array} \right| = ad - bc
1\times 2-7\times 0
Any expression multiplied by 1 remains the same
2-7\times 0
Any expression multiplied by 0 equals 0
2-0
Removing 0 doesn't change the value,so remove it from the expression
2
\begin{align}&D=1\\&D_{1}=9\\&D_{2}=2\end{align}
\text{Since }D\neq 0\text{,Cramer's rule can be applied, so find }y,x\text{ using the formulas }y=\frac{D_{1}}{D},x=\frac{D_{2}}{D}
\left\{ \begin{array}{l}y=9\\x=2\end{array}\right.
Find the intersection
\left\{ \begin{array}{l}x=2\\y=9\end{array}\right.
Check the solution
More Steps
Check the solution
\left\{ \begin{array}{l}9=2+7\\2=2\end{array}\right.
Simplify
\left\{ \begin{array}{l}9=9\\2=2\end{array}\right.
Evaluate
\textrm{true}
\left\{ \begin{array}{l}x=2\\y=9\end{array}\right.
Solution
\left(x,y\right) = \left(2,9\right)
Show Solutions
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