1.Solve the simultaneous equations:
5x + 4y = 13
3x + 8y = 5
Where do you get the -2?
Multiply * -2 (5x + 4y = 13)
-10x - 8y = -26
3x + 8y = 5
-7x = - 21
x = 3
substitute x = 3 in one of the equations and solve for y
Step 1: Let's solve the simultaneous equations using the method of substitution.
Step 2: Solve one equation for one variable in terms of the other variable. Let's solve the first equation for x:
5x + 4y = 13
Rearrange the equation:
5x = 13 - 4y
Divide both sides by 5:
x = (13 - 4y) / 5
Step 3: Substitute the expression for x in the second equation:
3( (13 - 4y) / 5 ) + 8y = 5
Step 4: Simplify the equation:
(39 - 12y) / 5 + 8y = 5
Multiply both sides by 5 to get rid of the denominator:
39 - 12y + 40y = 25
Combine like terms:
28y = -14
Step 5: Divide both sides by 28 to solve for y:
y = -14 / 28
Simplify:
y = -0.5
Step 6: Substitute the value of y back into the expression for x:
x = (13 - 4(-0.5)) / 5
Simplify:
x = (13 + 2) / 5
x = 15 / 5
x = 3
Step 7: The solution to the simultaneous equations is x = 3 and y = -0.5.
To solve the simultaneous equations, you can use either the substitution method or the elimination method. Let's solve the equations using the elimination method:
First, multiply the first equation by 8 and the second equation by 4 to make the coefficients of y in both equations the same:
8(5x + 4y) = 8(13)
4(3x + 8y) = 4(5)
This simplifies the system to:
40x + 32y = 104
12x + 32y = 20
Next, subtract the second equation from the first equation to eliminate y:
(40x + 32y) - (12x + 32y) = 104 - 20
This simplifies to:
28x = 84
Now, divide both sides of the equation by 28 to solve for x:
28x/28 = 84/28
This gives us:
x = 3
Next, substitute the value of x back into either of the original equations to solve for y. Let's use the first equation:
5x + 4y = 13
Substituting x = 3:
5(3) + 4y = 13
15 + 4y = 13
Now, isolate y by subtracting 15 from both sides:
4y = 13 - 15
4y = -2
Finally, divide both sides of the equation by 4 to solve for y:
y = -2/4
y = -1/2
Therefore, the solution to the simultaneous equations is x = 3 and y = -1/2.