Question

question
solve the system of equations $2x - 3y = 4$ and $9x - 8y = -26$ by combi equations.
(2x - 3y = 4)
(9x - 8y = -26)
$4x - 6y = 8$
$9x - 8y = -26$
\overline{
$x + \square y = \square$
} try

Explanation:

Step1: Multiply the first equation

We have the system of equations:

$$
LATEXBLOCK0
$$

Multiply equation (1) by 9 and equation (2) by 2 to make the coefficients of \(x\) the same:

$$
LATEXBLOCK1
$$

Step2: Subtract the equations

Subtract the new equation (1) from the new equation (2) to eliminate \(x\):

$$ (18x - 16y) - (18x - 27y) = -52 - 36 $$

Simplify the left - hand side and the right - hand side:

$$ 18x - 16y - 18x + 27y=-88 $$

$$ 11y=-88 $$

Step3: Solve for y

Divide both sides of the equation \(11y = - 88\) by 11:

$$ y=\frac{-88}{11}=-8 $$

Step4: Substitute y into equation (1)

Substitute \(y = - 8\) into equation (1) \(2x-3y = 4\):

$$ 2x-3\times(-8)=4 $$

$$ 2x + 24 = 4 $$

Subtract 24 from both sides:

$$ 2x=4 - 24=-20 $$

Divide both sides by 2:

$$ x=\frac{-20}{2}=-10 $$

Answer:

The solution of the system of equations is \(x=-10,y = - 8\)