Solve the system of equations using substitution: y = 4x - 10 y = 3x - 5
Understand the Problem
The question asks us to solve a system of two linear equations using the substitution method. We are given two equations, both solved for 'y' in terms of 'x'. We need to find the values of 'x' and 'y' that satisfy both equations simultaneously. This will involve substituting one equation into the other to solve for one variable, and then substituting that value back into either equation to solve for the other variable.
Answer
$(5, 10)$
Answer for screen readers
$(5, 10)$
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: $$4x - 10 = 3x - 5$$
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Solve for $x$ Subtract $3x$ from both sides: $$4x - 3x - 10 = 3x - 3x - 5$$ $$x - 10 = -5$$ Add 10 to both sides: $$x - 10 + 10 = -5 + 10$$ $$x = 5$$
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Substitute $x$ back into one of the original equations to solve for $y$ Let's use the second equation, $y = 3x - 5$: $$y = 3(5) - 5$$ $$y = 15 - 5$$ $$y = 10$$
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Write the solution as a coordinate pair The solution is $(x, y) = (5, 10)$.
$(5, 10)$
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 substitute the $x$ value into the wrong equation when solving for $y$, or to make an arithmetic error when solving for either $x$ or $y$. Another common mistake is to write the coordinates in the wrong order (i.e., (y, x) instead of (x, y)).
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