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Completion requirements
Solve the given system of equations by substitution. Verify the solution.
\(\left\{ \begin{array}{l}
x + y = 29 \\
x - y = 175 \end{array} \right.\)
Try to solve the given system of equations by substitution before continuing with the lesson.
\(\left\{ \begin{array}{l}
y = x^2 + 5x + 6 \\
y = 2x^2 + 4x - 6 \end{array} \right.\)
\(\left\{ \begin{array}{l}
x + y = 29 \\
x - y = 175 \end{array} \right.\)
\(\begin{align}
x + y &= 29 \\
x &= 29 - y \end{align}\)
\(\begin{align}
x - y &= 175 \\
\left( {29 - y} \right) - y &= 175 \\
29 - 2y &= 175 \\
- 2y &= 146 \\
y &= - 73 \end{align}\)
\(\begin{align}
x &= 29 - y \\
x &= 29 - \left( { - 73} \right) \\
x &= 102 \end{align}\)
The solution is \((102, –73)\).
Verify the solution.
x + y &= 29 \\
x &= 29 - y \end{align}\)
\(\begin{align}
x - y &= 175 \\
\left( {29 - y} \right) - y &= 175 \\
29 - 2y &= 175 \\
- 2y &= 146 \\
y &= - 73 \end{align}\)
\(\begin{align}
x &= 29 - y \\
x &= 29 - \left( { - 73} \right) \\
x &= 102 \end{align}\)
The solution is \((102, –73)\).
Verify the solution.
| Left Side | Right Side |
|---|---|
|
\(\begin{array}{r} x + y \\ 102 + \left( { - 73} \right) \\ 29 \end{array}\) |
\(29\) |
|
LS = RS |
|
| Left Side | Right Side |
|---|---|
|
\[\begin{array}{r} x - y \\ 102 - \left( { - 73} \right) \\ 175 \end{array}\] |
\(175\) |
|
LS = RS |
|
Try to solve the given system of equations by substitution before continuing with the lesson.
\(\left\{ \begin{array}{l}
y = x^2 + 5x + 6 \\
y = 2x^2 + 4x - 6 \end{array} \right.\)