Solve the following simultaneous equations: 7x−3y=2, 4x−5y=−12 2x+y=4, 5x+2y=−4 2x+3y=10 6x−3y=−21 x=2, y=4…

Question

Solve the following simultaneous equations: 7x−3y=2, 4x−5y=−12 2x+y=4, 5x+2y=−4 2x+3y=10 6x−3y=−21 x=2, y=4 x=1, y=2 x=2, y=2 x=−2, y=3

ScanSolve AI Tutor · Accepted Answer

Let's solve the system of simultaneous equations for part (b).

The given equations are:

7x - 3y = 2 \quad \text{(1)}

4x - 5y = -12 \quad \text{(2)}

Multiply equation (1) by 5 and equation (2) by 3 to make the coefficients of $y$ equal.
$5 \times (7x - 3y) = 5 \times 2 \Rightarrow 35x - 15y = 10 \quad \text{(3)}$ $3 \times (4x - 5y) = 3 \times (-12) \Rightarrow 12x - 15y = -36 \quad \text{(4)}$
Subtract equation (4) from equation (3) to eliminate $y$ .
$(35x - 15y) - (12x - 15y) = 10 - (-36)$ $35x - 15y - 12x + 15y = 10 + 36$ $23x = 46$
Solve for $x$ .
$x = \frac{46}{23}$ $x = 2$
Substitute the value of $x$ into equation (1) to find $y$ .
$7(2) - 3y = 2$ $14 - 3y = 2$ $-3y = 2 - 14$ $-3y = -12$
Solve for $y$ .
$y = \frac{-12}{-3}$ $y = 4$
The solution is:
$x=2, y=4$

Solve the following simultaneous equations: 7x−3y=2, 4x-5y=-12 2x+y=4, 5x+2y=-4 2x+3y=10 6x-3y=-21 x=2, y=4 x=1, y=2 x=2, y=2 x=-2, y=3