The ordered pair is (–1, –2)
Solution:
Given system of linear equations are
4x –7y = 10 – – – – (1)
3x + 2y = –7 – – – – (2)
To solve this by elimination method.
First multiply equation (1) by 3 and then multiply equation (2) by 4.
(1) × 3 ⇒ 12x –21y = 30 – – – – (3)
(2) × 4 ⇒ 12x + 8y = –28 – – – – (4)
Subtract equation (4) from equation (3), we get
⇒ 12x –21y – (12x + 8y) = 30 – (–28)
⇒ 12x –21y – 12x – 8y = 30 + 28
Combine like terms together.
⇒ 12x – 12x –21y – 8y = 30 + 28
⇒ –29y = 58
Divide both sides by –29, we get
⇒ y = –2
Substitute y = –2 in equation (1), we get
(1) ⇒ 4x –7y = 10
⇒ 4x – 7(–2) = 10
⇒ 4x + 14 = 10
⇒ 4x = 10 – 14
⇒ 4x = –4
Divide both side by 4, we get
⇒ x = –1
Hence the ordered pair for the given system of equations is (–1, –2).
