Solve the following system of equations using substitution: y = -3x + 5 y = -5x + 7
Understand the Problem
The question asks to solve a system of two linear equations using the substitution method. The equations are y = -3x + 5 and y = -5x + 7. We need to find the values of x and y that satisfy both equations.
Answer
$(1, 2)$
Answer for screen readers
$(1, 2)$
Steps to Solve
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Set the equations equal to each other Since both equations are equal to $y$, we can set them equal to each other: $$-3x + 5 = -5x + 7$$
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Solve for $x$ Add $5x$ to both sides of the equation: $$-3x + 5 + 5x = -5x + 7 + 5x$$ $$2x + 5 = 7$$ Subtract 5 from both sides: $$2x + 5 - 5 = 7 - 5$$ $$2x = 2$$ Divide both sides by 2: $$\frac{2x}{2} = \frac{2}{2}$$ $$x = 1$$
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Substitute the value of $x$ back into either equation to solve for $y$ Let's use the first equation: $y = -3x + 5$. Substitute $x = 1$: $$y = -3(1) + 5$$ $$y = -3 + 5$$ $$y = 2$$
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Write the solution as an ordered pair The solution is $(x, y) = (1, 2)$.
$(1, 2)$
More Information
The solution to the system of equations is the point where the two lines intersect. The intersection occurs at the point (1, 2), meaning that $x = 1$ and $y = 2$ satisfy both equations.
Tips
A common mistake is making errors when combining like terms or when performing the arithmetic operations when solving for $x$ and $y$. Another common mistake is forgetting to substitute the value of $x$ back into one of the original equations to find the value of $y$. Always double-check calculations and make sure to solve for both variables.
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