Question

find the solution of the system of equations.
$3x - 4y = -29$
$6x + 5y = -32$
answer attempt 1 out of 2
(\square,\square) submit answer

Explanation:

Step1: Eliminate $x$ variable

Multiply first equation by $-2$:
$-2(3x - 4y) = -2(-29)$
$\implies -6x + 8y = 58$

Step2: Add to second equation

Add the new equation to $6x + 5y = -32$:
$(-6x + 8y) + (6x + 5y) = 58 + (-32)$
$\implies 13y = 26$

Step3: Solve for $y$

Divide both sides by 13:
$y = \frac{26}{13} = 2$

Step4: Substitute $y=2$ into first equation

Plug $y=2$ into $3x - 4y = -29$:
$3x - 4(2) = -29$
$\implies 3x - 8 = -29$

Step5: Solve for $x$

Add 8 to both sides, then divide by 3:
$3x = -29 + 8 = -21$
$\implies x = \frac{-21}{3} = -7$

Answer:

$(-7, 2)$