Solve the following system of equations using substitution: 3x - 7y = -10 x - y = -6
Understand the Problem
The question asks 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.
Answer
$(-8, -2)$
Answer for screen readers
$(-8, -2)$
Steps to Solve
- Isolate $x$ in the second equation
We start with the second equation: $x - y = -6$
Add $y$ to both sides to isolate $x$: $x = y - 6$
- Substitute $x$ into the first equation
Now substitute $x = y - 6$ into the first equation $3x - 7y = -10$: $3(y - 6) - 7y = -10$
- Solve for $y$
Expand and simplify the equation: $3y - 18 - 7y = -10$ $-4y - 18 = -10$
Add 18 to both sides: $-4y = 8$
Divide by -4: $y = -2$
- Solve for $x$
Substitute $y = -2$ back into the equation $x = y - 6$: $x = -2 - 6$ $x = -8$
$(-8, -2)$
More Information
The solution to the system of equations is $x = -8$ and $y = -2$. This means that the point $(-8, -2)$ is the intersection of the two lines represented by the given equations.
Tips
A common mistake is to incorrectly substitute the expression for $x$ or $y$ into the wrong equation or to make an algebraic error when simplifying. Also, be careful with the signs (positive or negative) when moving terms from one side of the equation to the other.
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