y=4x+5, y=x+5 solve it
Understand the Problem
The problem asks us to solve a system of two linear equations. We can use substitution or elimination to find the values of x and y that satisfy both equations.
Answer
$x = 3$, $y = 1$
Answer for screen readers
$x = 3$, $y = 1$
Steps to Solve
- Solve for $x$ by adding the two equations
Add the two equations together to eliminate $y$: $$ (2x + y) + (x - y) = 7 + 2 $$ This simplifies to: $$ 3x = 9 $$
- Solve for $x$
Divide both sides of the equation by 3: $$ x = \frac{9}{3} = 3 $$
- Solve for $y$ by substituting $x$ into one of the equations
Substitute $x = 3$ into the second equation $x - y = 2$: $$ 3 - y = 2 $$
- Isolate $y$
Subtract 3 from both sides: $$ -y = 2 - 3 $$ $$ -y = -1 $$
- Solve for $y$
Multiply both sides by -1: $$ y = 1 $$
$x = 3$, $y = 1$
More Information
We can check our answer by substituting $x = 3$ and $y = 1$ into both original equations: $2(3) + 1 = 6 + 1 = 7$, which is correct. $3 - 1 = 2$, which is also correct.
Tips
A common mistake is making errors in arithmetic when adding or subtracting the equations, or when substituting the value of one variable into another equation. It's important to double-check each step to avoid these mistakes. Another common mistake is not distributing the negative sign correctly when using elimination.
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