Answer:
[tex]x = 1.5[/tex]
[tex]y =1[/tex]
Step-by-step explanation:
Given
[tex]4x + 2y = 8[/tex]
[tex]6x - 4y = 5[/tex]
Required
Solve for x and y
[tex]4x + 2y = 8[/tex] --- (1)
[tex]6x - 4y = 5[/tex] --- (2)
Divide equation (1) through by 2
[tex]\frac{1}{2}(4x + 2y) = 8*\frac{1}{2}[/tex]
[tex]2x + y = 4[/tex]
Make y the subject
[tex]y = 4 - 2x[/tex]
Substitute 4 - 2x for y in equation (2)
[tex]6x - 4y = 5[/tex]
[tex]6x - 4(4- 2x) = 5[/tex]
Open bracket
[tex]6x - 16+ 8x = 5[/tex]
Collect Like Terms
[tex]6x + 8x = 5+16[/tex]
[tex]14x = 21[/tex]
Solve for x
[tex]x = \frac{21}{14}[/tex]
[tex]x = 1.5[/tex]
Substitute 1.5 for x in [tex]y = 4 - 2x[/tex]
[tex]y = 4 - 2(1.5)[/tex]
[tex]y = 4 - 3[/tex]
[tex]y =1[/tex]
To check the solution:
Substitute the values of x and y i the equations
[tex]4x + 2y = 8[/tex]
[tex]4 * 1.5 + 2 * 1 = 8[/tex]
[tex]8 = 8[/tex]
[tex]6x - 4y = 5[/tex]
[tex]6 * 1.5 - 4 * 1 = 5[/tex]
[tex]5 = 5[/tex]
Hence, the solution is true
