To find the solution of the system of equations, we can use the method of substitution or elimination.
Method of substitution:
1. Solve one equation for one variable in terms of the other variable. Let's solve the first equation for y:
2x - y = -7
y = 2x + 7
2. Substitute the expression for y in terms of x into the second equation:
4x - (2x + 7) = -4
4x - 2x - 7 = -4
2x - 7 = -4
3. Add 7 to both sides:
2x = 3
4. Divide both sides by 2:
x = 3/2 = 1.5
5. Substitute the value of x back into the expression for y in terms of x:
y = 2(1.5) + 7
y = 3 + 7
y = 10
Therefore, the solution to the system of equations is x = 1.5 and y = 10.
Method of elimination:
1. Multiply the first equation by 2 and the second equation by 1 so that the coefficients of y will be the same:
2(2x - y) = 2(-7)
4x - 2y = -14
1(4x - y) = 1(-4)
4x - y = -4
2. Subtract the second equation from the first equation to eliminate the y variable:
(4x - 2y) - (4x - y) = -14 - (-4)
4x - 2y - 4x + y = -14 + 4
-y = -10
3. Multiply both sides by -1 to isolate the y variable:
y = 10
4. Substitute the value of y back into one of the original equations. Let's use the first equation:
2x - y = -7
2x - 10 = -7
5. Add 10 to both sides:
2x = 3
6. Divide both sides by 2:
x = 3/2 = 1.5
Again, the solution to the system of equations is x = 1.5 and y = 10.
what is the solution of the system
2x-y=-7
4x-y=-4
1 answer