solve the simultaneous equations to find the coordinates of the point of intersection for the pair of lines of the simultaneous equations. Then check the answer by graphing the equations
3x-y=-4
2x-y=0
3x-y=-4
2x-y=0
-3x+y=4
-x=4
x=-4
Plug that back into either equation to solve for y.
Second equation:
2x-y=0, 2x=y, y=2x
Firs equation:3x-y=-4
3x-y=3x-2x= x=-4 x=-4
y=2x=2*(-4)=-8 y=-8
Check of result:
First equation:
3x-y=3*(-4)-(-8)=-12+8=-4
Second equation:
2x-y=2*(-4)-(-8)=-8+8=0
To solve the given simultaneous equations, you can use the method of substitution or the method of elimination. I will explain both methods, and then you can choose the one you are more comfortable with.
Method 1: Substitution
Step 1: Solve one equation for one variable in terms of the other variable. Let's solve the second equation for y.
2x - y = 0
y = 2x
Step 2: Substitute the expression for y from Step 1 into the other equation.
3x - (2x) = -4
x - 4 = -4
x = 0
Step 3: Substitute the value of x into either of the original equations to solve for y.
2(0) - y = 0
-y = 0
y = 0
The coordinates of the point of intersection are (x, y) = (0, 0).
Method 2: Elimination
Step 1: Multiply one or both of the equations by suitable constants to make the coefficients of one of the variables the same or opposite.
Let's multiply the second equation by 3 to eliminate y.
3(2x - y) = 3(0)
6x - 3y = 0
Step 2: Add or subtract the equations to eliminate one of the variables.
(6x - 3y) - (3x - y) = 0 - (-4)
6x - 3y - 3x + y = 4
3x - 2y = 4
Step 3: Solve the resulting equation for one variable.
3x - 2y = 4
y = (3x - 4) / 2
Step 4: Substitute the expression for y into either of the original equations to solve for the other variable.
3x - [(3x - 4) / 2] = -4
6x - (3x - 4) = -8
6x - 3x + 4 = -8
3x + 4 = -8
3x = -12
x = -4
Step 5: Substitute the value of x into the expression for y to find the other variable.
y = (3(-4) - 4) / 2
y = -16 / 2
y = -8
Again, we get the coordinates of the point of intersection as (x, y) = (-4, -8).
To check the answer by graphing the equations:
1. Plot both equations on a graph.
2. The point at which the two lines intersect is the solution to the simultaneous equations.
3. The coordinates of the point of intersection obtained from solving the equations, (0, 0) and (-4, -8), should match with the point of intersection on the graph.
I hope this helps! Let me know if you have any further questions.