Question

12. Solve the simultaneous equations.
2x + 3y = 10
3x + 5y = 17

Answer 1

Answer:

$x = -1$, $y = 4$

Step-by-step explanation:

$2x + 3y = 10$

$3x + 5y = 17$

By using substitution:

$2x + 3y = 10$

$2x = -3y + 10$

$x = -\frac{3}{2} y + 5$

$3x + 5y = 17$

$3 (-\frac{3}{2}y + 5) + 5y = 17$

$\frac{1}{2} y + 15 = 17$

$\frac{1}{2} y = 2$

$y = 4$

$x = -\frac{3}{2}y + 5$

$x = -\frac{3}{2} (4) + 5$

$x = -1$

Answer 2

2x=10-3y; x=(10-3y)/2;
plug in the value of x into the second equation:
3((10-3y)/2)+5y=17 then solve for y:
(30-9y)/2+5y=17
(30-9y)2+10y/2=17
(30+y)2=17
30+y=17/2
y=8.5-30
y=-21.5 plug the value of y into the previous equation and solve for x
x=(10-3y)/2
x=(10-3(-21.5))/2
x=74.5/2
x=37.25