Solve the pairs of simultaneous equations by the substitution method.
5x-9y=17
3x-8y=5
2x+4y=8
3x+4y=16
4x+7y=15
5x+9y=,19
To solve the pair of simultaneous equations by the substitution method, follow these steps:
Step 1: Choose one of the equations and solve it for one variable in terms of the other variable.
Let's solve the first equation (5x-9y=17) for x:
5x = 9y + 17
x = (9y + 17) / 5
Step 2: Substitute the expression from step 1 into the other equation.
Substitute x = (9y + 17) / 5 into the second equation (3x-8y=5):
3((9y + 17) / 5) - 8y = 5
Step 3: Simplify and solve the equation.
Multiply throughout by 5 to get rid of the fraction:
3(9y + 17) - 40y = 25
27y + 51 - 40y = 25
-13y = -26
y = 2
Step 4: Substitute the value of y into the expression from step 1 to find x.
x = (9y + 17) / 5
x = (9(2) + 17) / 5
x = 19 / 5
Therefore, the solution to the simultaneous equations is x = 19/5 and y = 2.
(poor method for this particular question, but ...)
solve the second for x, (I look for the smallest coefficient)
3x = 5+8y
x = (5+8y)/3
sub into the first
5(5+8y)/3 - 9y = 17
multiply by 3 to eliminate fractions
5(5+8y) - 27y = 51
25 + 40y - 27y = 51
13y = 26
y = 2
then x = (5+16)/3 = 7