Selesaikan setiap persamaan linear serentak yang berikut dengan menggunakan kaedah penghapusan. Solve each of…

Question

Selesaikan setiap persamaan linear serentak yang berikut dengan menggunakan kaedah penghapusan. Solve each of the following simultaneous linear equations by using elimination method.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for the simultaneous linear equations using the elimination method.

1. Solve:

x - y = 6 \quad (1)

2x + y = 3 \quad (2)

Add equation (1) and equation (2) to eliminate $y$ .
$(x - y) + (2x + y) = 6 + 3$ $3x = 9$
Solve for $x$ .
$x = \frac{9}{3}$ $x = 3$
Substitute $x = 3$ into equation (1).
$3 - y = 6$ $-y = 6 - 3$ $-y = 3$ $y = -3$
The solution is $\boxed{x = 3, y = -3}$ .

2. Solve:
$5x - 2y = 5 \quad (1)$ $3x - 2y = -1 \quad (2)$
Subtract equation (2) from equation (1) to eliminate $y$ .
$(5x - 2y) - (3x - 2y) = 5 - (-1)$ $5x - 2y - 3x + 2y = 5 + 1$ $2x = 6$
Solve for $x$ .
$x = \frac{6}{2}$ $x = 3$
Substitute $x = 3$ into equation (1).
$5(3) - 2y = 5$ $15 - 2y = 5$ $-2y = 5 - 15$ $-2y = -10$
Solve for $y$ .
$y = \frac{-10}{-2}$ $y = 5$
The solution is $\boxed{x = 3, y = 5}$ .

3. Solve:
$5x - 2y = 6 \quad (1)$ $2x + 3y = 10 \quad (2)$
Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of $y$ equal.
$3 \times (5x - 2y) = 3 \times 6 \implies 15x - 6y = 18 \quad (3)$ $2 \times (2x + 3y) = 2 \times 10 \implies 4x + 6y = 20 \quad (4)$
Add equation (3) and equation (4) to eliminate $y$ .
$(15x - 6y) + (4x + 6y) = 18 + 20$ $19x = 38$
Solve for $x$ .
$x = \frac{38}{19}$ $x = 2$
Substitute $x = 2$ into equation (2).
$2(2) + 3y = 10$ $4 + 3y = 10$ $3y = 10 - 4$ $3y = 6$
Solve for $y$ .
$y = \frac{6}{3}$ $y = 2$
The solution is $\boxed{x = 2, y = 2}$ .

4. Solve:
$4x - 5y = 13 \quad (1)$ $2x - 3y = 7 \quad (2)$
Multiply equation (2) by 2 to make the coefficients of $x$ equal.
$2 \times (2x - 3y) = 2 \times 7 \implies 4x - 6y = 14 \quad (3)$
Subtract equation (3) from equation (1) to eliminate $x$ .
$(4x - 5y) - (4x - 6y) = 13 - 14$ $4x - 5y - 4x + 6y = -1$ $y = -1$
Substitute $y = -1$ into equation (2).
$2x - 3(-1) = 7$ $2x + 3 = 7$ $2x = 7 - 3$ $2x = 4$
Solve for $x$ .
$x = \frac{4}{2}$ $x = 2$
The solution is $\boxed{x = 2, y = -1}$ .

Selesaikan setiap persamaan linear serentak yang berikut dengan menggunakan kaedah penghapusan. Solve each of the following simultaneous linear equations by using elimination method.

Step-by-step solution

Add equation (1) and equation (2) to eliminate $y$ .

Solve for $x$ .

Substitute $x = 3$ into equation (1).

Subtract equation (2) from equation (1) to eliminate $y$ .

Solve for $x$ .

Substitute $x = 3$ into equation (1).

Solve for $y$ .

Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of $y$ equal.

Add equation (3) and equation (4) to eliminate $y$ .

Solve for $x$ .

Substitute $x = 2$ into equation (2).

Solve for $y$ .

Multiply equation (2) by 2 to make the coefficients of $x$ equal.

Subtract equation (3) from equation (1) to eliminate $x$ .

Substitute $y = -1$ into equation (2).

Solve for $x$ .

Still stuck on this one?

More Mathematics Questions

Selesaikan setiap persamaan linear serentak yang berikut dengan menggunakan kaedah penghapusan. Solve each of the following simultaneous linear equations by using elimination method.

Step-by-step solution

Add equation (1) and equation (2) to eliminate yyy.

Solve for xxx.

Substitute x=3x = 3x=3 into equation (1).

Subtract equation (2) from equation (1) to eliminate yyy.

Solve for xxx.

Substitute x=3x = 3x=3 into equation (1).

Solve for yyy.

Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of yyy equal.

Add equation (3) and equation (4) to eliminate yyy.

Solve for xxx.

Substitute x=2x = 2x=2 into equation (2).

Solve for yyy.

Multiply equation (2) by 2 to make the coefficients of xxx equal.

Subtract equation (3) from equation (1) to eliminate xxx.

Substitute y=−1y = -1y=−1 into equation (2).

Solve for xxx.

Still stuck on this one?

More Mathematics Questions

Add equation (1) and equation (2) to eliminate $y$ .

Solve for $x$ .

Substitute $x = 3$ into equation (1).

Subtract equation (2) from equation (1) to eliminate $y$ .

Solve for $x$ .

Substitute $x = 3$ into equation (1).

Solve for $y$ .

Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of $y$ equal.

Add equation (3) and equation (4) to eliminate $y$ .

Solve for $x$ .

Substitute $x = 2$ into equation (2).

Solve for $y$ .

Multiply equation (2) by 2 to make the coefficients of $x$ equal.

Subtract equation (3) from equation (1) to eliminate $x$ .

Substitute $y = -1$ into equation (2).

Solve for $x$ .