Need help,i need to find the ordered pair.
3x+2y=40 and 2x + 3y =230/19
then i get stuck. please show the steps.
To find the ordered pair that satisfies both equations, you can use a method called substitution or elimination. Let's use the substitution method for this example.
Step 1: Rearrange one of the equations to solve for one variable in terms of the other. Let's rearrange the first equation, 3x + 2y = 40, to solve for x.
3x = 40 - 2y
x = (40 - 2y) / 3
Step 2: Substitute the expression for x in the second equation. Plug in (40 - 2y) / 3 for x in the second equation, 2x + 3y = 230/19.
2((40 - 2y) / 3) + 3y = 230/19
Step 3: Simplify the equation.
(80 - 4y) / 3 + 3y = 230/19
To get rid of the fractions, we can multiply each term by the common denominator, which is 3 * 19 = 57.
57 * ((80 - 4y) / 3) + 57 * 3y = 57 * (230/19)
(57 * (80 - 4y) / 3) + 57 * 3y = 230
Step 4: Simplify further.
57(80 - 4y) + 171y = 230 * 3
4560 - 228y + 171y = 690
Combine like terms:
-57y = -3870
Step 5: Solve for y.
Divide both sides of the equation by -57:
y = -3870 / -57
Simplifying this expression, we get:
y = 70
Step 6: Substitute the value of y back into one of the original equations to solve for x. We can use the rearranged first equation for this.
x = (40 - 2y) / 3
x = (40 - 2(70)) / 3
x = (40 - 140) / 3
x = -100 / 3
Step 7: Write the ordered pair.
The ordered pair is (-100/3, 70).