Question

systems of equations with elimination cha
solve the system of equations.
$-5y + 6x = 40$
$3y - 8x = -46$
$x = square$
$y = square$

Explanation:

Step1: Align equations, label them

Equation 1: $6x - 5y = 40$
Equation 2: $-8x + 3y = -46$

Step2: Eliminate $y$, scale equations

Multiply Eq1 by 3: $18x - 15y = 120$
Multiply Eq2 by 5: $-40x + 15y = -230$

Step3: Add scaled equations

$(18x - 15y) + (-40x + 15y) = 120 + (-230)$
$18x - 40x = -110$
$-22x = -110$

Step4: Solve for $x$

$x = \frac{-110}{-22} = 5$

Step5: Substitute $x=5$ into Eq1

$6(5) - 5y = 40$
$30 - 5y = 40$

Step6: Solve for $y$

$-5y = 40 - 30$
$-5y = 10$
$y = \frac{10}{-5} = -2$

Answer:

$x=5$
$y=-2$