Question

solve the system - elimination
solve the system of equations by using elimination.
demonstrate your work in the space to the left.
5x + 6y = 50
x - 6y = -26
write your answer below using an ordered pair (x, y).

Explanation:

Step1: Add the two equations to eliminate \( y \)

The two equations are:
\( 5x + 6y = 50 \)
\( x - 6y = -26 \)

Adding them together: \((5x + 6y) + (x - 6y) = 50 + (-26)\)
Simplify the left side: \(5x + x + 6y - 6y = 6x\)
Simplify the right side: \(50 - 26 = 24\)
So we get \(6x = 24\)

Step2: Solve for \( x \)

Divide both sides of \(6x = 24\) by 6: \(x=\frac{24}{6}=4\)

Step3: Substitute \( x = 4 \) into one of the original equations to solve for \( y \)

Let's use the second equation \(x - 6y = -26\). Substitute \(x = 4\):
\(4 - 6y = -26\)
Subtract 4 from both sides: \(-6y = -26 - 4\)
Simplify the right side: \(-6y = -30\)
Divide both sides by -6: \(y=\frac{-30}{-6}=5\)

Answer:

\((4, 5)\)