Question

solve the system of equations.
$7y + 10x = -11$
$4y - 3x = -15$
$x = square$
$y = square$
show calculator

Explanation:

Step1: Align equations for elimination

Label equations:
$$10x + 7y = -11 \quad (1)$$
$$-3x + 4y = -15 \quad (2)$$

Step2: Eliminate $x$ via scaling

Multiply (1) by 3, (2) by 10:
$$30x + 21y = -33 \quad (3)$$
$$-30x + 40y = -150 \quad (4)$$

Step3: Add (3) and (4)

Sum to eliminate $x$:
$$(30x-30x)+(21y+40y)=-33-150$$
$$61y = -183$$

Step4: Solve for $y$

Divide by 61:
$$y = \frac{-183}{61} = -3$$

Step5: Substitute $y=-3$ into (2)

Find $x$ using equation (2):
$$-3x + 4(-3) = -15$$
$$-3x -12 = -15$$

Step6: Solve for $x$

Isolate $x$:
$$-3x = -15 + 12$$
$$-3x = -3$$
$$x = \frac{-3}{-3} = 1$$

Answer:

$x = 1$
$y = -3$