Solve the following system of equations: y=x+1, y=-x+5
Understand the Problem
The question provides two linear equations and implies that we need to solve for x and y. This is a system of equations problem, and we can solve for it using substitution or elimination.
Answer
$x = 3$, $y = 2$
Answer for screen readers
$x = 3$, $y = 2$
Steps to Solve
- Solve the first equation for y Isolate $y$ in the first equation $x + y = 5$ by subtracting $x$ from both sides:
$x + y - x = 5 - x$
$y = 5 - x$
- Substitute into the second equation Substitute the expression for $y$ from step 1 into the second equation $3x - 2y = 5$:
$3x - 2(5 - x) = 5$
- Simplify and solve for x Distribute the $-2$ and simplify:
$3x - 10 + 2x = 5$
Combine like terms ($3x$ and $2x$):
$5x - 10 = 5$
Add $10$ to both sides:
$5x = 15$
Divide by $5$:
$x = 3$
- Solve for y Substitute the value of $x$ back into either of the original equations or the equation from step 1. Using $y = 5 - x$:
$y = 5 - 3$
$y = 2$
$x = 3$, $y = 2$
More Information
We solved a system of two linear equations with two variables, $x$ and $y$. The solution represents the point of intersection of the two lines when graphed.
Tips
A common mistake is to incorrectly distribute the negative sign when substituting $y$ into the second second equation. For example, forgetting to distribute the $-2$ to both terms in $(5-x)$ would lead to an incorrect $x$ value. Another common mistake is an arithmetic error when simplifying the equations.
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