Solve the following system of equations.
4x+9y=10 x=
5x+18y=19 y=
1st times 2
8x + 18y = 20
5x + 18y = 19
subtract them
3x = 1
x = 1/3
sub x = 1/3 into the 1st and solve for y
to get y = 26/27
To solve the given system of equations, we will use the method of substitution.
Step 1: Begin with the first equation, 4x + 9y = 10, and solve it for x in terms of y.
4x = 10 - 9y (subtract 9y from both sides)
x = (10 - 9y)/4 (divide both sides by 4)
Step 2: Substitute the expression for x in terms of y into the second equation, 5x + 18y = 19.
5((10 - 9y)/4) + 18y = 19
Step 3: Simplify and solve for y.
Distribute 5 to ((10 - 9y)/4) and combine like terms:
(50 - 45y)/4 + 18y = 19
Multiply through by 4 to remove the denominator:
50 - 45y + 72y = 76
Combine like terms:
27y = 26
Divide both sides by 27:
y ≈ 0.963
Step 4: Substitute the value of y back into the expression for x to find x.
x = (10 - 9(0.963))/4 ≈ 0.24
Therefore, the solution to the given system of equations is x ≈ 0.24 and y ≈ 0.963.