Solve the following system of simultaneous equations graphically: 2x + 3y = 8 and 3x + 2y = 7

Question

ScanSolve AI Tutor · Accepted Answer

The problem asks to solve the simultaneous equations graphically. Since I cannot perform graphical plotting directly, I will solve the first pair of equations () using an algebraic method (elimination method), which is a common way to solve such problems.

The system of equations for is:

2x + 3y = 8 \quad (1)

3x + 2y = 7 \quad (2)

Multiply the equations to make the coefficients of one variable equal.
To eliminate $y$ , multiply equation (1) by 2 and equation (2) by 3:
$2 \times (2x + 3y) = 2 \times 8 \implies 4x + 6y = 16 \quad (3)$ $3 \times (3x + 2y) = 3 \times 7 \implies 9x + 6y = 21 \quad (4)$
Subtract equation (3) from equation (4) to eliminate $y$ .
$(9x + 6y) - (4x + 6y) = 21 - 16$ $9x - 4x + 6y - 6y = 5$ $5x = 5$
Solve for $x$ .
$\frac{5x}{5} = \frac{5}{5}$ $x = 1$
Substitute the value of $x$ into one of the original equations to find $y$ .
Using equation (1):
$2(1) + 3y = 8$ $2 + 3y = 8$ $3y = 8 - 2$ $3y = 6$
Solve for $y$ .
$\frac{3y}{3} = \frac{6}{3}$ $y = 2$
The solution to the system of equations is $x=1$ and $y=2$ .
$x=1, y=2$

Solve the following system of simultaneous equations graphically: 2x + 3y = 8 and 3x + 2y = 7

Answer

Step-by-step solution

Multiply the equations to make the coefficients of one variable equal.

Subtract equation (3) from equation (4) to eliminate $y$ .

Solve for $x$ .

Substitute the value of $x$ into one of the original equations to find $y$ .

Solve for $y$ .

Try one yourself

Still stuck on this one?

More Mathematics Questions

Solve the following system of simultaneous equations graphically: 2x + 3y = 8 and 3x + 2y = 7

Answer

Step-by-step solution

Multiply the equations to make the coefficients of one variable equal.

Subtract equation (3) from equation (4) to eliminate yyy.

Solve for xxx.

Substitute the value of xxx into one of the original equations to find yyy.

Solve for yyy.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Subtract equation (3) from equation (4) to eliminate $y$ .

Solve for $x$ .

Substitute the value of $x$ into one of the original equations to find $y$ .

Solve for $y$ .