Question
uestion
ind the solution of the system of
quations.
ind the solution of the system of
quations.
Ask by Delgado Sullivan. in the United States
Mar 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
La solución es
y
.
Solution
Solve the system of equations
.
Solve the system of equations by following steps:
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
- step1: Solve the equation:
- step2: Substitute the value of
- step3: Simplify:
- step4: Multiply both sides of the equation by LCD:
- step5: Simplify the equation:
- step6: Move the constant to the right side:
- step7: Subtract the numbers:
- step8: Divide both sides:
- step9: Divide the numbers:
- step10: Substitute the value of
- step11: Calculate:
- step12: Calculate:
- step13: Check the solution:
- step14: Rewrite:
La solución del sistema de ecuaciones es.
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Bonus Knowledge
To find the solution of the system of equations, you can use either the substitution method or the elimination method. Let’s use elimination! First, multiply the second equation by 5 to align the coefficients of x:
Now, add the two equations:
This simplifies to:
Now, rearranging gives us:
Now we’ll return to the original second equation. Let’s express
in terms of
using the second equation:
Now substitute this expression into equation (1):
Multiply everything by 3 to eliminate the fraction:
Expanding:
Combining like terms:
Thus,
Now substitute
back into the expression for
:
So, the solution of the system of equations is
.