Let’s solve the system of equations step by step, following the instructions provided. The equations given are:
- \( 10x - 8y = -2 \) (Equation 1)
- \( 9x + 8y = 59 \) (Equation 2)
Which variable will you eliminate?
Since the coefficients of \( y \) in Equation 1 and Equation 2 are opposites (i.e., -8 and +8), we will eliminate variable \( y \).
Add the two equations:
Adding Equation 1 and Equation 2:
\[ (10x - 8y) + (9x + 8y) = -2 + 59 \]
\[ 10x + 9x - 8y + 8y = -2 + 59 \]
\[ 19x = 57 \]
Solve the equation for x. Show your work:
To find \( x \), divide both sides by 19:
\[ x = \frac{57}{19} \]
Calculating gives:
\[ x = 3 \]
Substitute that value for x into either equation and solve for y. Show your work:
Now we substitute \( x = 3 \) into one of the original equations. We can use Equation 2:
\[ 9(3) + 8y = 59 \]
Calculating gives:
\[ 27 + 8y = 59 \]
Now, subtract 27 from both sides:
\[ 8y = 59 - 27 \]
\[ 8y = 32 \]
Then divide both sides by 8:
\[ y = \frac{32}{8} = 4 \]
Write your solution as an ordered pair (x, y):
The solution to the system of equations is:
\[ (x, y) = (3, 4) \]
Use substitution to check your solution for the system. Show your work:
We can verify the solution \( (3, 4) \) by substituting it back into both equations.
- For Equation 1:
\[ 10(3) - 8(4) = -2 \]
Calculating:
\[ 30 - 32 = -2 \]
This is true, so Equation 1 holds.
- For Equation 2:
\[ 9(3) + 8(4) = 59 \]
Calculating:
\[ 27 + 32 = 59 \]
This is also true, so Equation 2 holds.
Final Answers:
The solution to the system is \( (3, 4) \).
1 answer