Solve the following system of equations using substitution: y = -5x - 9 y = 2x - 2
Understand the Problem
The question asks 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. The provided equations are y = -5x - 9 and y = 2x - 2.
Answer
$(-1, -4)$
Answer for screen readers
$(-1, -4)$
Steps to Solve
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Set the two equations equal to each other Since both equations are solved for $y$, we can set them equal to each other: $$-5x - 9 = 2x - 2$$
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Solve for x Add $5x$ to both sides of the equation, then add $2$ to both sides. Finally, divide by 7. $$-5x - 9 + 5x = 2x - 2 + 5x$$ $$-9 = 7x - 2$$ $$-9 + 2 = 7x - 2 + 2$$ $$-7 = 7x$$ $$x = -1$$
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Substitute the value of x back into one of the original equations to solve for y Let's use the second equation, $y = 2x - 2$: $$y = 2(-1) - 2$$ $$y = -2 - 2$$ $$y = -4$$
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Write the solution as an ordered pair (x, y) The solution is $x = -1$ and $y = -4$.
$(-1, -4)$
More Information
The solution to the system of equations is the point where the two lines intersect on a graph.
Tips
A common mistake is to incorrectly solve for x or y due to arithmetic errors. Ensure to double-check your work when isolating variables. Also, remember to substitute the value of $x$ back into one of the original equations to find the value of $y$. In some cases, students solve only $x$ and forget about $y$.
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