Solve the system by substitution: -2x - 7 = y, 4x + 3y = -3.
Understand the Problem
The question is asking to solve a system of equations using the substitution method. It involves two equations: one equation gives 'y' in terms of 'x' and the other is a linear equation in 'x' and 'y'.
Answer
The final solution is given as an ordered pair $(x, y)$.
Answer for screen readers
The solution to the system of equations will be provided in the form of ordered pair $(x, y)$.
Steps to Solve
- Isolate 'y' in the first equation
First, we need to write down the first equation provided. Let's say it's in the form $y = mx + b$.
- Substitute 'y' in the second equation
Now we'll take the expression for 'y' from the first equation and substitute it into the second equation. If the second equation is in the form $ax + by = c$, we can replace 'y' with the expression we found in step 1.
- Solve for 'x'
After substituting 'y', we should now have an equation with only 'x'. We'll solve this equation for 'x', isolating it on one side. This might involve rearranging the equation and simplifying.
- Find 'y' using the value of 'x'
Once we have the value of 'x', we'll take that value and substitute it back into the first equation $y = mx + b$ to find the corresponding 'y' value.
- Write the final solution
Finally, write down the solution in an ordered pair form, typically $(x, y)$.
The solution to the system of equations will be provided in the form of ordered pair $(x, y)$.
More Information
Using the substitution method is a systematic way to find a single solution for a system of linear equations. It can be especially useful when one of the equations is already solved for one variable.
Tips
- Forgetting to substitute correctly, leading to new equations that are not equivalent.
- Miscalculating when isolating variables, which can lead to incorrect values for 'x' or 'y'.
- Not double-checking the final solution by plugging the values into original equations.
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