Solve the following system of equations using substitution: x + y = -6 x + 6y = 14
Understand the Problem
This question requires us to solve a system of two linear equations using the substitution method. We need to find the values of x and y that satisfy both equations:
x + y = -6 x + 6y = 14
The end result will be of the format (x, y).
Answer
$(-10, 4)$
Answer for screen readers
$(-10, 4)$
Steps to Solve
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Solve the first equation for $x$ To isolate $x$ in the equation $x + y = -6$, subtract $y$ from both sides: $x = -6 - y$
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Substitute the expression for $x$ into the second equation Replace $x$ in the equation $x + 6y = 14$ with the expression we found in step 1: $(-6 - y) + 6y = 14$
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Solve the resulting equation for $y$ Simplify and solve for $y$: $-6 - y + 6y = 14$ $5y = 20$ $y = \frac{20}{5}$ $y = 4$
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Substitute the value of $y$ back into the expression for $x$ Substitute $y = 4$ into $x = -6 - y$: $x = -6 - 4$ $x = -10$
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Write the solution as an ordered pair The solution is $x = -10$ and $y = 4$. Therefore, the ordered pair is $(-10, 4)$.
$(-10, 4)$
More Information
The solution $(-10, 4)$ is the point where the two lines $x + y = -6$ and $x + 6y = 14$ intersect on the Cartesian plane.
Tips
A common mistake is to incorrectly substitute the value of $y$ back into the equation for $x$ or to make errors in the algebraic manipulation when solving for $x$ or $y$. Careful attention to signs and correct application of algebraic rules can help avoid these mistakes.
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