Add the equations: 4a + 4a - 5b + 5b = 7 + 17
ie 8a = 24
a = 3, so b = 1
8.00 − 5.91 = 2.09 (Method is to first subtract 2.09 from 8.00, which equals 5.91 If you then subtract 5.91 from 8.00 the answer will be 2.09)
x - y = 2 : Equation 1 2x + 3y = 4 : Equation 2 Multiplying Equation 1 by 3 gives 3x - 3y = 6 : Equation 3 Adding Equation 2 to Equation 3 gives 5x = 10 Dividing both sides by 5 gives x = 5 Substituting x=5 into Equation 1 gives 5 - y = 2 Therefore y = 3. Our final answer is therefore x=5 and y=3
This might refer to the method used to solve an equation. Take, for example, the equation: 2x + 1 = 15 To solve this for x, the "x" must be isolated on the left. The multiplication and addition must be "undone" - that is, the inverse operation must be applied. Also, since multiplication is carried out before addition, this "undoing" should be applied in the inverse order - in this case, undo the addition first. What you end up doing, in this case, is first, subtract one from both sides, leaving you with: 2x = 14 and then, divide both sides by 2.
5x + 3y = -63x - 2y = 4 (multiply by 2 the first equation, multiply by 3 the second equation)10x + 6y = -129x - 6y = 12 (add both the equations)19x = 0 (divide by 19 both sides)x = 0 (substitute 0 for x into the first equation)5x + 3y = -65(0) + 3y = -63y = -6 (divide by 3 to both sides)y = -2Thus, (0, -2) is the solution of the given system of the equations.
Substitution method: from first equation y = 5x - 8. In the second equation this gives 25x - 5(5x - 8) = 32 ie 25x - 25x + 40 = 32 ie 40 = 32 which is not possible, so the system has no solution. Multiplication method: first equation times 5 gives 25x - 5y = 40, but second equation gives 32 as the value of the identical expression. No solution.
x=1, y=1
Double first equation: 2x + 2y = 4 Subtract this from second equation giving 5y = 5 so y = 1 and x = 1
You need two equations to use the addition method.
solve system equation using addition method 3x-y=9 2x+y=6
From first equation, -y = 3x + 3. Substitute in second equation: -3x + 5(3x + 3) = -21 ie 12x = -36 so x = -3 and y = -(-9 + 3) = 6. Easier method: subtract first equation from second giving -4y = -24 so y = 6, this in first equation gives -6 = 3x + 3, ie 3x = -9 so x = -3
8.00 − 5.91 = 2.09 (Method is to first subtract 2.09 from 8.00, which equals 5.91 If you then subtract 5.91 from 8.00 the answer will be 2.09)
x+y=5
the answer
z=pq
The answer depends on the equation: there is no single method which can be used for all equations.
x - y = 2 : Equation 1 2x + 3y = 4 : Equation 2 Multiplying Equation 1 by 3 gives 3x - 3y = 6 : Equation 3 Adding Equation 2 to Equation 3 gives 5x = 10 Dividing both sides by 5 gives x = 5 Substituting x=5 into Equation 1 gives 5 - y = 2 Therefore y = 3. Our final answer is therefore x=5 and y=3
how do you use the substitution method for this problem 2x-3y=-2 4x+y=24