Solve the following set of equations. Can I use y = mx + b to calculate the equation
4x−y = 6
2x + 3y = 5
re-arrange the first to say:
y = 4x-6
Now sub that into the 2nd:
2x + 3(4x-6) = 5
solve for x, then sub into y = 4x-6
or
write down the first:
4x - y = 6
double the second:
4x + 6y = 10
subtract them:
-7y = -4
y = 4/7
sub back into the first
you should of course get the same answers.
I solved for x and got x = 23/14
Is this right
To solve the set of equations, we'll use the method of substitution.
Step 1: Solve the first equation for one variable in terms of the other.
We have the equation: 4x - y = 6
Rearranging the equation, we get: -y = -4x + 6
Multiplying both sides by -1 gives: y = 4x - 6
Step 2: Substitute the expression for y obtained in step 1 into the second equation.
We have the equation: 2x + 3y = 5
Now substitute y with 4x - 6: 2x + 3(4x - 6) = 5
Step 3: Solve the equation obtained in step 2 for x.
Expanding the equation, we get: 2x + 12x - 18 = 5
Combining like terms, we have: 14x - 18 = 5
Adding 18 to both sides: 14x = 23
Dividing both sides by 14: x = 23/14
Step 4: Substitute the value of x obtained in step 3 into either of the original equations to find y.
Using the first equation, substitute x with 23/14: 4(23/14) - y = 6
Multiply 4 by 23/14: (92/14) - y = 6
Simplifying the fraction: 46/7 - y = 6
Subtracting 46/7 from both sides: -y = 6 - 46/7
Finding a common denominator: -y = 42/7 - 46/7
Combining fractions: -y = -4/7
Multiplying both sides by -1: y = 4/7
So the solution to the set of equations is:
x = 23/14
y = 4/7
To answer your question, you cannot directly use the equation y = mx + b to solve this set of equations. This equation represents the equation of a straight line, where m is the slope and b is the y-intercept. However, to solve a system of equations, you need to use methods like substitution or elimination as shown above.