What is the solution of the system?

Solution of system of linear equation y = 2x – 4 and 3x - 2y = 8 is x = 0 and y = -4

Solution:

Need to determine solution of following system of linear equation

y = 2x – 4    (1)

3x - 2y = 8   (2)

If we observe the equation (1), we can say that we are having value of y in terms of x. so substitution method is the best approach to solve the above system of linear equation.

In substitution method, we will substitute value of y in equation (2) in terms of variable x from equation (1)  

On substituting y = 2x – 4 in equation (2) , we get equation in one variable that is x which is as follows

3x – 2 (2x – 4 )   = 8    

=> 3x – 4x + 8 = 8

=> -x = 8 – 8  

=> x = 0

On substituting x = 0 in equation (1), we get  

y = 2 x 0 – 4

=> y = -4

Hence solution of system of linear equation y = 2x – 4 and 3x - 2y = 8 is x = 0 and y = -4

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.