Solve the system by substitution: y = -7x + 6 and y = -10x.
Understand the Problem
The question is asking to solve a system of equations using the substitution method. The equations given are y = -7x + 6 and y = -10x. To solve them, we will set the two expressions for y equal to each other and solve for x, then substitute back to find the corresponding y value.
Answer
The solution is $(-2, 20)$.
Answer for screen readers
The solution to the system of equations is $(-2, 20)$.
Steps to Solve
- Set the equations equal to each other
Since both equations equal $y$, we can set them equal to each other: $$ -7x + 6 = -10x $$
- Solve for x
Next, we'll isolate $x$ by adding $10x$ to both sides: $$ -7x + 10x + 6 = 0 $$ This simplifies to: $$ 3x + 6 = 0 $$ Now, subtract 6 from both sides: $$ 3x = -6 $$ Finally, divide by 3: $$ x = -2 $$
- Substitute x back into one of the original equations
We can substitute $x = -2$ back into either of the original equations to find $y$. Let's use $y = -10x$: $$ y = -10(-2) $$
- Compute the value of y
Multiplying gives us: $$ y = 20 $$
- Write the solution as an ordered pair
The solution to the system of equations is the point where the two lines intersect, which is: $$ (-2, 20) $$
The solution to the system of equations is $(-2, 20)$.
More Information
The solution $(-2, 20)$ represents the point where the two lines defined by the equations intersect. This means that, at $x = -2$, both equations yield $y = 20$.
Tips
- Forgetting to simplify the equation properly when combining like terms.
- Using the wrong equation to substitute back for $y$, which could lead to an incorrect value.
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