Answer:
The correct solutions are (6, -2).
Step-by-step explanation:
For the first equation, rearrange to make x the subject.
3x + 4y = 10
[tex]3x = 10 -4y[/tex]
Divide the whole equation by 3 to isolate x:
[tex]3x = 10 -4y\\3x \div 3 = \frac{10}{3} - \frac{4}{3}y\\x = \frac{10}{3} - \frac{4}{3}y\\[/tex]
Now substitute this into the second equation:
[tex]6x - 2y = 40\\6(\frac{10}{3} - \frac{4}{3}y) - 2y = 40\\6(\frac{10}{3}) + 6(\frac{4}{3}) - 2y = 40[/tex]
[tex]20 - 8y - 2y = 40\\20 - 10y = 40[/tex]
Subtract 20 from both sides:
20 - 10y = 40
20 - 10y - 20 = 40 - 20
-10y = 20
Divide both sides by 2:
-10y ÷ 10 = 20 ÷ 10
-y = 2 ∴ y = -2
Plug this value back into the first equation:
3x + 4y = 10
3x + 4(-2) = 10
3x + (-8) = 10
3x - 8 = 10
Add 8 to both sides:
3x - 8 + 8 = 10 + 8
3x = 18
Divide both sides by 3:
3x ÷ 3 = 18 ÷ 3
x = 6
Therefore, the correct solutions are (6, -2).
Hope this helps!
