Solve by substitution..

y=4x-7 and 2x-3y=6

This is the only question i am stuck on, please help..

make one equation = 0

so 2(0)-3y=6

3y/3=6/3
y=2

now
2x-3(2)=6
2x-6=6
2x=6+6
2x=12
2x/2=12/2
x=6

now sub that it to the other side

y=4(6)-7
y=24-7
y=17

2=4x-7
2+7=4x
9=4x
9/4=4x/4
2.25=x

Since it says Solve by substitution..

y=4x-7
2x-3y=6

just substitute in 4x-7 for y in the 2nd equation:

2x-3(4x-7) = 6
2x-12x+21 = 6
-10x = -15
x = 3/2
y = 4x-7 = 4(3/2)-7 = 6-7 = -1

Paul's solution method is strange (and wrong). Using the intercepts will not help in finding the intersection.

To solve this system of equations by substitution, we can start by solving one of the equations for one variable in terms of the other variable, and then substitute that expression into the other equation.

Let's solve the first equation for x:
y = 4x - 7

Adding 7 to both sides:
y + 7 = 4x

Dividing both sides by 4:
(1/4)(y + 7) = x

Now we have an expression for x in terms of y. We can substitute this value into the second equation.

Substitute (1/4)(y + 7) for x in the second equation:
2(1/4)(y + 7) - 3y = 6

Simplify, distribute 2/4 and -3:
(1/2)(y + 7) - 3y = 6
(1/2)y + 7/2 - 3y = 6

Combine like terms:
(1/2)y - 3y + 7/2 = 6

Multiply by 2 to get rid of the fractions:
y - 6y + 7 = 12
-5y + 7 = 12

Subtract 7 from both sides:
-5y = 5

Divide by -5 to solve for y:
y = -1

Now that we have the value of y, we can substitute it back into the first equation to solve for x:
y = 4x - 7
-1 = 4x - 7

Add 7 to both sides:
6 = 4x

Divide by 4 to solve for x:
x = 6/4
x = 3/2

Therefore, the solution to the system of equations is x = 3/2 and y = -1.

To solve the system of equations by substitution, follow these steps:

Step 1: Solve one of the equations for one variable in terms of the other variable. Let's solve the first equation, y = 4x - 7, for y.

y = 4x - 7

Step 2: Substitute the expression for y from step 1 into the second equation. Replace every occurrence of y in the second equation with the expression 4x - 7.

2x - 3(4x - 7) = 6

Step 3: Simplify the equation by distributing the -3 to each term inside the parentheses.

2x - 12x + 21 = 6

Step 4: Combine like terms on the left side of the equation.

-10x + 21 = 6

Step 5: Move the constant term (21) to the right side of the equation by subtracting it from both sides.

-10x = 6 - 21
-10x = -15

Step 6: Divide both sides of the equation by -10 to isolate x.

x = -15 / -10
x = 3/2 or 1.5

Step 7: Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation, y = 4x - 7.

y = 4(1.5) - 7
y = 6 - 7
y = -1

Therefore, the solution to the system of equations is x = 1.5 and y = -1.